無限可積分系通信 (Infinite Analysis News Letters)
- Documents of past years :
1996
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INFINITE ANALYSIS NEWS LETTER No. 279 December 10, 1997
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Seminar Information
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日本数学会 1998 年度年会の講演申し込みのお願い
野海（神戸大・理）です。来年春の学会の予定は
期間： 1998 年 3 月26日(木) -- 29日(日)
場所： 名城大学 (名古屋市天白区塩釜口)
となっています。「無限可積分系セッション」は継続しますので、
今まで通り多数の方が講演の申し込みをして下さるようお願いします。
申込の締め切りは 12 月 16 日 (火) です。
講演の申し込みをされる方は、お忘れなく。
1997 年 12 月 10 日 野海正俊
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INFINITE ANALYSIS NEWS LETTER No. 278 November 21, 1997
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Seminar Information
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Infinite Analysis Seminar
===========================
日本数学会 1998 年度年会について
野海（神戸大・理）です。ご存じのように、来年春の学会の予定は
期間： 1998 年 3 月26日(木) -- 29日(日)
場所： 名城大学 (名古屋市天白区塩釜口)
となっています。「無限可積分系セッション」は継続しますので、
今まで通り多数の方が講演の申し込みをして下さるようお願いします。
申込の締め切りは 12 月 16 日 (火) です。
お忘れなく。
(1) 「無限可積分系セッション」の特別講演について
いつも通り 2 件、特別講演を設けたいと思いますが、
「 X 氏に Y についての特別講演をお願いしたら」等のご意見を、
セッション責任者まで、
お知らせ下さい。責任者の周辺で検討して決めます。
12 月 5 日までに日本数学会に連絡しなければいけないのですが、
本人と連絡を取る時間が必要ですので、ご希望のある方は、早急に
(遅くとも 11 月28日頃までに) お知らせ下さい。
(2) 企画特別講演について
日本数学会から、企画特別講演の候補者推薦依頼が来ています。
推薦する候補者について、ご意見をお持ちの方はご連絡下さい。
意見のある方は、こちらも早急にお願いします。
企画特別講演は 96 年春に企画特別講演が設けられて以来、96 年
秋の 50 周年記念のときを除いて、「無限可積分系」からの推薦は
行っていません。セッション責任者としては、毎回、セッションの
特別講演の方を優先して考えていますので、特に希望がなければ、
企画特別講演の推薦はしないつもりです。(責任者の方で候補者を
考えて依頼するようなことは敢えてしない ---と言う意味。)
以上よろしくご協力下さい。
なお、今回までは私が責任者をやりますが、前の上野喜三雄さんから
責任者を引き継いで 2 年になりますので次回からどなたかに交代して
もらうつもりでいます。これについてはまた追ってご連絡します。
1997 年 11 月 21 日 野海正俊
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INFINITE ANALYSIS NEWS LETTER No. 277 November 19, 1997
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Seminar Information
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Infinite Analysis Seminar
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Time: December 4 (Thu) 14:00-15:00
Place: Room 009, RIMS, Kyoto University
Speaker: Professor Masako Asaeda (University of Tokyo)
Title: Exotic subfactors with small index
Abstract:
Subfactors in the theory of operator algberas are related to
various other fields, and to 3-dimensional topological quantum
field theory, in particular, through $6j$-symbols.
Subfactors with index slightly larger than 4 would have exotic features
which do not arise from groups nor quantum groups, "if they exist".
The existence of such subfactors has been conjectured
since 1991 by Haagerup, and at the same time, one of them
was shown to exist by himself, but no other subfactors have been
found until recently.
In this seminar, I will explain the recent result proving the
existence of the second example, the most exotic one in Haagerup's
candidates. This is the joint work with Uffe Haagerup.
I will give a talk in Japanese, and write on the blackbord in English.
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INFINITE ANALYSIS NEWS LETTER No. 276 November 10, 1997
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Seminar Information
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Time : Nov. 13 (Thur.) 15:00 - 16:00
Place: Room 206, RIMS, Kyoto University
Speaker: Prof. Takeshi Hirai
Title: "On irreducible unitary representations of the
infinite symmetric group"
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INFINITE ANALYSIS NEWS LETTER No. 275 November 7, 1997
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Seminar Information
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Nov. 11 (Tue.) 16:30 - 17:30 Room 202, RIMS, Kyoto University
Prof. Grigori Olshanski
"Applications of shifted symmetric functions in
representation theory"
Nov. 13 (Thur.) 16:30 - 17:30 Room 102, RIMS, Kyoto University
Dr. Andreas Nilsson
"Multipliers on symmetric spaces"
Nov. 25 (Tue.) 16:30 - 17:30 Room 202, RIMS, Kyoto University
Prof. Eric Opdam
"Residue calculus for root systems"
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INFINITE ANALYSIS NEWS LETTER No. 274 October 29, 1997
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関係者各位殿：
さる 10 月 16 日に文部省で、重点領域研究231 「無限可積分系」
の最終ヒアリング行われ、無事終了しました。
ヒアリングに出席の学術審議会の委員の方々は、私たちの
成果に対して好意的であるとの印象を受けました。
これまでの皆様方のご協力に感謝します。
「無限可積分系」に関しては、来年３月に報告書を出せば
形式的には終了したことになります。しかしながら、今後も
基礎的な学問分野を特別領域研究（重点領域研究の名称が
変更されました）に引き続き採択してもらうためには、
「無限可積分系」の成果を非専門家にも分かる形で残すことが
大切と考えられます。英文の出版は準備中ですが、それとは
別に、和文の分かりやすい報告が必要であろうかと思われます。
このようなことを考え、来年２月に「無限可積分系」の
成果報告の最終シンポジウムを行い、それをまとめて出版する
ことを考えています。これは私個人の考えですので、皆様の
ご意見をお寄せください。
京都大学理学部数学教室
上野健爾
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INFINITE ANALYSIS NEWS LETTER No. 273 October 8, 1997
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Seminar Information
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Kobe Seminar on Hypergeometric Systems
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October 15 (Wed), 1997
Prof. Grigori OLSHANSKI (IPPI, Moscow/RIMS, Kyoto)
Asymptotics of Jack polynomials as the number of variables
goes to infinity
15:30-- / Room C501, Department of Mathematics, Kobe University
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For further information, contact:
Masatoshi NOUMI
Masahiko SAITO
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INFINITE ANALYSIS NEWS LETTER No. 268 September 15, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor Benjamin Enriquez
(Centre de Math., Ecole Polytechnique)
Time: September 19 (Fri), 12:00-13:00
Place: Room 102, RIMS, Kyoto University
Title: Coinvariants approach to the QKZ equations
Abstract: We present a quantum version of the construction of the
KZ system of equations as a flat connection on the spaces of coinvariants of
representations of tensor products of Kac-Moody algebras. We consider
here representations of a tensor product of Yangian doubles and compute
the coinvariants of a deformation of the subalgebra generated by the
regular functions of a rational curve with marked points. We observe
that Drinfeld's quantum Casimir element can be viewed as a deformation
of the zero-mode of the Sugawara tensor in the Yangian double. These
ingredients serve to define a compatible system of difference equations,
which we identify with the quantum KZ equations introduced by I. Frenkel
and N. Reshetikhin.
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INFINITE ANALYSIS NEWS LETTER No. 271 September 31, 1997
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Seminar Information
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Infinite Analysis Seminar
Time: October 6 (Mon), 14:00-15:00
Place: Room 115, RIMS, Kyoto University
Speaker: Professor Piotr Hajac
Title: Overview of the Quantum Double Torus
Abstract: Quantum double torus is defined as a disconnected quantum subgroup
of the pure twist q-deformation of U(2). It is a compact matrix quantum
group in the sense of S. Woronowicz, though q is unitary Hopf-Galois theory
point of view, the quantum double torus is a noncommutative cleft
$T^2$-Galois extension determined by a nontrivial cocycle and
the trivial actio
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INFINITE ANALYSIS NEWS LETTER No. 270 September 30, 1997
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Seminar Information
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Lectures
10/7(Tue) Prof. Eric Opdam
"On the Knizhnik Zamolodchikov equations
for complex reflection groups"
16:30 - 17:30 RIMS 202, Kyoto University
10/9(Thu) Prof. Grigori Olshanski
"Shifted Schur functions and their applications"
16:30 - 17:30 RIMS 005(?), Kyoto University
10/14(Tue) Prof. Eric Opdam
"Symmetries for fake degrees of complex reflection groups"
16:30 - 17:30 RIMS 202, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 269 September 18, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor Nikita Slavnov (Steklov Math. Inst.)
Time: September 22th (Mon) 14:00-15:00
Place: Room 115, RIMS, Kyoto University
Title: The Riemann-Hilbert problem associated with correlation
functions of the Quantum Nonlinear Schrodinger equation (QNLS).
Abstract: The correlation function of local fields is represented
in terms of a Fredholm determinant. The Riemann-Hilbert problem is
used for the description of the Fredholm determinant.
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INFINITE ANALYSIS NEWS LETTER No. 268 September 15, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor Benjamin Enriquez
(Centre de Math., Ecole Polytechnique)
Time: September 19 (Fri), 12:00-13:00
Place: Room 102, RIMS, Kyoto University
Title: Coinvariants approach to the QKZ equations
Abstract: We present a quantum version of the construction of the
KZ system of equations as a flat connection on the spaces of coinvariants of
representations of tensor products of Kac-Moody algebras. We consider
here representations of a tensor product of Yangian doubles and compute
the coinvariants of a deformation of the subalgebra generated by the
regular functions of a rational curve with marked points. We observe
that Drinfeld's quantum Casimir element can be viewed as a deformation
of the zero-mode of the Sugawara tensor in the Yangian double. These
ingredients serve to define a compatible system of difference equations,
which we identify with the quantum KZ equations introduced by I. Frenkel
and N. Reshetikhin.
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INFINITE ANALYSIS NEWS LETTER No. 267 August 21, 1997
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Seminar Information
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Date: August 26th (Tue)
Place: Room 202, RIMS, Kyoto University
14:00--15:00
Professor Sasha Voronov (MIT)
I. Semi-Infinite Induction and Wakimoto Modules
We suggest the construction and study properties of semi-infinite
induction, which relates to semi-infinite cohomology the same way
induction relates to homology and coinduction to cohomology. We prove a
version of the Shapiro Lemma, relating the semi-infinite cohomology of a
module with that of the semi--infinitely induced module. A practical
outcome of our construction is a simple construction of Wakimoto
modules, the highest-weight modules used in double-sided BGG resolutions
of irreducible modules.
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15:15--16:15
Professor Sasha Voronov (MIT)
II. Homotopy Gerstenhaber algebras and topological field theory
We discuss our joint result with T. Kimura and G. Zuckerman, which shows
that the BRST complex of a topological conformal field theory is a
homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in
1992. The method is based on operads, which will be introduced along the way.
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16:30--17:30
Professor Alexander Kogan (UC Berkeley)
q-deformation of W-algerbas
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INFINITE ANALYSIS NEWS LETTER No. 267 August 7, 1997
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Seminar Information
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Speaker: Professor Katsuhisa Mimachi
Kyushu University
Title: A solution of quantum KZ equation and its application to
eigenvalue problem of Macdonald type
Time: September 8 (Mon), 13:30-14:30
Place: Room 327, Department of Mathematics, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 266 July 30, 1997
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Seminar Information
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Speaker: Professor Guenter v.Gehlen
Physikalisches Institut der Universitaet Bonn, Germany
Title: Low-lying energy levels of the integrable Potts quantum chain
Time: July 31th (Thu), 11:00-12:00
Place: Room 402, RIMS, Kyoto University
******************************************************************************
Abstract:
We start with a review of the peculiar properties and of the analytic
results presently available of the superintegrable and integrable ${\bf Z}_N$
chiral Potts models.
Combining analytic and numerical results, we suggest an oscillatory
behaviour of the low-temperature spin-correlation function, with wave
vector exponent $\nu_s=N/2$ at the superintegrable self-dual temperature,
coinciding with Baxter's interface tension exponent.
In the non-superintegrable case, the only analytic result available for a
gap is the McCoy-Roan-formula. We review the hypotheses used in the
derivation. Using special parity symmetries at the boundary of the
hermitian region, we conjecture a high-temperature formula for the missing
rapidity-relation. Numerical results for the $Z_3$ to $Z_7$-cases show that the
McCoy-Roan formula, supplemented by our relation, describes various
non-trivial details of the momentum behaviour of the gap without any
parameter.
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INFINITE ANALYSIS NEWS LETTER No. 265 July 25, 1997
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Seminar Information
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Speaker: E. Corrigan
(Durham Univ.)
Title: Aspects of Integrability in the Presence
of Boundaries
Time: July 28th (Mon), 13:30-
Place: Room K206, Yukawa Institute, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 264 July 24, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor Seok-Jin Kang
(Seoul National Univ.)
Title: Supertrace formula for graded Lie superalgebras and Moonshine Problem
Time: July 28th (Mon), 14:00-15:00
Place: Room 005, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 263 July 14, 1997
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Seminar Information
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Infinite Analysis Seminar
Date : 14:00--15:00, July 22 (Tue), 1997
Place : Rm. 402(4th floor), RIMS, Kyoto University
Speaker: Prof Tudor Ratiu
Title : The doubel bracket equation, the dispersionless Toda PDE,
and the Kostant convexity theorem
Abstract:
The double bracket equation is a gradient vector field on
adjoint orbits of compact Lie algebras whose dynamics is completely
described in Lie theoretic terms. In addition, the finite non-periodic Toda
lattice can be written as a double bracket equation. In the limit, one gets
the dispersionless Toda PDE, aslo a completely integrable system.
In trying to analyze the scattering
behavior of its solutions, one is led to a generalization of Kostant's
convexity theorem for the group of area preservig diffeomorphisms of the
annulus.
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Date : 15:30--16:00, July 22 (Tue), 1997
Place : Rm. 402(4th floor), RIMS, Kyoto University
Speaker: Prof Tudor Ratiu
Title : Dissipation induced instability
Abstract:
In the Lyapunov stability analysis by energy methods, only sufficient
conditions can be obtained by determining the definiteness of the Hessian
at a critical point. If the Hessian is indefinite, the criterion is
inconclusive. It will be shown that for quite general types of dissipations,
these equlibria become spectrally unstable (exponentially growing modes)
for the perturbed dissipative system. Applications include the rigid body
with
rotors and a certain beam equation. The mathematical techniques are based on
normal forms for the Hessian and the symplecitc form at the relative
equilibrium, combined with a judicious choice of Lyapunov function.
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Date : 13:30--15:00, July 25 (Fri), 1997
Place : Rm. 102(1st floor), RIMS, Kyoto University
Speaker: Prof Tudor Ratiu
Title : Shadowing curves for two dimensional Navier-Stokes equation
Abstract:
The Euler euqations for two dimensional homogeneous incompressible
fluids admit a large family of stationary solutions. Among these are the
vorticities that are eigenfucntions of the Laplacian. These flows are the
two dimensional analogs of the Arnold-Beltrami-Childress (ABC) flows. For
the first eigenvalue, the corresponding vorticity is a global minimum of
the enstrophy restricted to the level set of the energy and is hence stable
in the sense of Lyapunov. It turns out that for any initial condition of the
Navier-Stokes equation in a conical domain determined by the second
eigenvalue
of the Laplacian, the solution if the Navier-Stokes equation is attracted
by the manifold of these stable ABC flows along a shadowing curve
in such a way that one can give a precise exponential type estimate
of the error.
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INFINITE ANALYSIS NEWS LETTER No. 262 July 4, 1997
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Announcement
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日本数学会の一般講演の申し込みについて
秋の学会（東大・駒場）の一般講演の申し込みの締め切りが
迫っています。７月７日（月）が締め切りとなっていますの
で、一般講演を考えていてまだ申し込みをしていない方は、
大至急講演申し込みをして下さい。よろしくお願いします。
「無限可積分系セッション」 野海正俊（神戸大学）
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INFINITE ANALYSIS NEWS LETTER No. 261 July 2, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor Boris Feigin
Title: Modular functors, the quantum groups at the roots of unity, etc.
Date: July 4 (Fri) 16:00-17:30: Room 102, RIMS, Kyoto Unviersity
July 7 (Mon) 17:30-19:00: Room 009, RIMS, Kyoto Unviersity
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Speaker: Professor Nicholai Reshetikhin
Title: TBA
Date: July 4 (Fri) 14:00-15:30: Room 102, RIMS, Kyoto Unviersity
July 7 (Mon) 10:00-11:30: Room 102, RIMS, Kyoto Unviersity
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INFINITE ANALYSIS NEWS LETTER No. 260 July 2, 1997
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Seminar Information
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Infinite Analysis Seminar
Title: The decomposition of level-1 irreducible highest weight modules
with respect to the level-0 actions of the quantum affine algebra
$U'_q(\hat{sl}_n)$
Speaker: Koichi Takemura (RIMS)
Date: July 4 (Fri) 12:00-13:00
Room: Room 102, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 259 June 20, 1997
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INFINITE ANALYSIS LECTURE NOTE
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"Infinite Analysis Lecture Note No. 15"
is available now.
Author: 大槻知忠
Title : 量子不変量をめぐる３次元位相幾何学の
組み合わせ的方法
Price : 500 yen
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INFINITE ANALYSIS NEWS LETTER No. 258 June 19, 1997
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Announcements
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秋の学会について
ご存じのように、９７年度の日本数学会秋季総合分科会は
東京大学（駒場キャンパス）において
９月３０日から１０月３日の日程で
行われます。（詳しくは「数学通信」今年５月の号の５１頁
以降を参照。）
「無限可積分系セッション」も継続しますので、一般講演の
申し込みを多数お寄せ下さるようお願いします。申し込みは
秋季総合分科会長宛で、
締め切りは７月７日（必着）
となっていますので、お忘れなく。また
１）「企画特別講演」への推薦（無限可積分系からの）
２）無限可積分系セッションの「特別講演」
について、講演者・内容等についての希望がありましたら、
６月２０日頃までに、野海まで e-mail でお知らせ下さい。
よろしくお願いします。
野海正俊（神戸大学）
==========================================================
"Program of INTEGRABLE SYSTEMS AND ALGEBRAIC GEOMETRY"
\documentstyle[12pt]{article}
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\begin{document}
\begin{center}
\large
{\bf Taniguchi Symposium}\\
\vspace{0.2cm}
{\it INTEGRABLE SYSTEMS AND ALGEBRAIC GEOMETRY}
\end{center}
\begin{flushright}
June, 11, 1997
\end{flushright}
\vspace{2mm}
{\bf Organizers} \quad
Masa-Hiko Saito (Kobe), Yuji Shimizu(Kyoto), Kenji Ueno (Kyoto)
\begin{description}
\item[1.Date]
July, 7 (Mo), 1997 -- July 11 (Fr), 1997.
\item[2.Place:]
Room 420, RIMS, Kyoto University, Kyoto, Japan
Telephone: 075--753--7206
\item[3.Program：]
\end{description}
\smallskip
\addtolength{\textwidth}{50pt}
\noindent
July, 7, (Monday)
\begin{itemize}
\item 13:30 -- 14:30: \quad B.Dubrovin (SISSA, Trieste) \\
On Algebraic Solutions of Certain
Painlev\'e-VI Differential Equations
\item 14:45 --15:45: \quad M. Noumi \& Y. Yamada, (Kobe) \\
Some remarks on integrable hierarchy
associated with Gauss-Manin system
\item 16:00 -- 17:00: \quad T. Maeno, (Kyoto) \\
Extended Bruhat ordering and quantum Schubert
calculus
\end{itemize}
\smallskip
\noindent
July, 8, (Tuesday)
\begin{itemize}
\item 9:30--10:30: \quad Y.Namikawa, (Sophia Univ., Tokyo) \\
A construction of flops by deformation
theory
\item 10:45--11:45: \quad V.Batyrev (T\"ubingen) \\
String-theoretic Hodge numbers of singular varieties
\item 13:30 -- 14:30: \quad J.Stienstra (Utrecht)\\
Hypergeometric functions, mixed motives, and
mirror symmetry
\item 14:45 --15:45: \quad M.-H.Saito, (Kobe) \\
Mordell-Weil lattices and mirror symmetry
\item 16:00 -- 17:00: \quad A. Miwa, (Kyoto)\\
On a compactification of families of Calabi-Yau
hypersurfaces in toric varieties
\end{itemize}
\smallskip
\newpage
\noindent
July, 9, (Wednesday)
\begin{itemize}
\item 9:30--10:30: \quad M.Kobayashi,(Tokyo Inst. of Tech.)\\
On real slice of modification
\item 10:45--11:45: \quad M.Kapranov (Northwestern)\\
Hecke operators related to 2-dimensional local fields
\item 13:30 -- 14:30: \quad T. Terasoma, (Tokyo)\\
Local systems and algebraic correspondence
for hypergeometric functions
\item 14:45 --15:45: \quad Y.Shimizu, (Kyoto) \\
A cohomology class arising from conformal field
theory
\item 16:00 -- 17:00: \quad H. Umemura (Nagoya)\\
Some aspects of special polynomials associated with the Painlev\'e
equations
\end{itemize}
\smallskip
\noindent
July, 10, (Thursday)
\begin{itemize}
\item 9:30--10:30: \quad S. Mukai, (Nagoya)\\
Complete moduli of abelian surfaces and
regular polyhedra
\item 10:45--11:45: \quad E.Getzler (Northwestern) \\
Topological recursion relations in genus
2
\item 13:30 -- 14:30: \quad T. Eguchi, (Tokyo) \\
Quantum cohomology and Virasoro algebra
\item 14:45 --15:45: \quad M.Gross (Cornell) \\
The Strominger-Yau-Zaslow Mirror Symmetry
Construction
\item 16:00 -- 17:00: \quad T.Kawai, (RIMS, Kyoto)
\\ Elliptic genus
\smallskip
\end{itemize}
\noindent
July, 11, (Friday)
\begin{itemize}
\item 9:30--10:30: \quad S. Hosono, (Toyama) \\
Type IIA monodromy of Calabi-Yau manifolds
\item 10:45--11:45: \quad R.Donagi (IAS \& Pennsylvania)\\
Some Integrable Systems in High Energy Physics
\end{itemize}
\noindent
Please see also Home Pages \newline
http://www.math.s.kobe-u.ac.jp/HOME/mhsaito/index.html, \newline
http://www.math.s.kobe-u.ac.jp/HOME/mhsaito/rimspg.html, \newline
which is updated from time to time.
\end{document}
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INFINITE ANALYSIS NEWS LETTER No. 257 June 6, 1997
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Seminar Information
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Series of lectures by V. Tarasov,
Title : q-hypergeometric functions and representation theory
Place : Room 3311, Department of Mathematics, Graduate School of Mathematics
Kyushu University, Hakozaki Fukuoka
Dates : June 13 (Fri) -- June 15 (Sun)
The first lecture will start at 16:00 June 13.
Further schedule will be fixed later.
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INFINITE ANALYSIS NEWS LETTER No. 256 May 22, 1997
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Seminar Information
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Infinite Analysis Seminar
Title: K- theory and Cherednik's double affine Hecke algebra
Speaker: I. Grojnowski
Date: May 23 (Fri) 14:00-15:00
Room: Room 102, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 255 May 19, 1997
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Seminar Information
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Infinite Analysis Seminar
Date:
May 30 (Fri) 13:30-15:00, 16:00-17:30 Room 102, RIMS, Kyoto Univ.
May 31 (Sat) 13:30-15:00, 16:00-17:30 Room 102, RIMS, Kyoto Univ.
June 3 (Tue) 13:30-15:00, 16:00-17:30 Room 402, RIMS, Kyoto Univ.
June 4 (Wed) 13:30-15:00, 16:00-17:30 Room 102, RIMS, Kyoto Univ.
Title:
R-Matrix Kac-Moody algebras, Knizhnik-Zamolodchikov equations
and the elliptic quantum many-body problem
Speaker:
Ivan Cherednik (Univ. of North Carolina at Chapel Hill)
Abstract:
The mini-course will be devoted to r-martrix Knizhnik-Zamolodchikov
equations their relations to Kac-Moody algebras and applications to
"elliptic radial parts" (the Olshanetsky-Perelomov operators and
generalizations).
The first day's lectures
will be about general concept of r-matrix (for arbitrary root
systems) and its Kac-Moody interpretation in the case of "A".
We will consider the rational and trigonometric cases in detail and
establish relations to the so-called KZB. The main theorem here is that the
coinvariant (tau-function) satisfies the corresponding r-matrix KZ-equation.
The second will be devoted to integral formulas for r-KZ.
We will formulate and prove the key lemma about coinvariants which
governs integral formulas for both KZ and its stationary variant
and can be naturally extended to KZB.
The third are about the construction of OP-type operators for arbitrary
r-matrix based on the double affine Dunkl operators. The relations with
double affine KZ will be also esatblished (Matsuo like isomorphism).
Here the main point is to switch to affine root systems and ensure the
convergence.
The last will contain some discussion. For
instance, we will give the formula for the "critical level" in the spherical
case. Then we will consider the difference operators using the double affine
Hecke algebras.
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INFINITE ANALYSIS NEWS LETTER No. 254 April 30, 1997
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Seminar Information
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Kobe Seminar on Hypergeometric Systems
------------------------------------------------------
May 6(Tue), 1997 (15:30--)
Masa-Hiko SAITO (Kobe University)
Prepotentials of Yukawa couplings and
lattice theta functions
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May 20(Tue), 1997 (15:30--)
Hiraku NAKAJIMA (Kyoto University)
Hilbert schemes of points on algebraic surfaces
and Jack polynomials
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Room C501/Department of Mathematics, Kobe University
For further information, contact:
Masatoshi NOUMI
Masa-Hiko SAITO
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INFINITE ANALYSIS NEWS LETTER No. 253 April 28, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Mr. Michael Kleber (UC, Berkeley)
Title: Decomposition of representations of Yangians
Time: May 1 (Thur), 14:00-15:00
Place: Room 009, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 252 April 22, 1997
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Seminar Information
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Kobe Seminar on Hypergeometric Systems
(Room C501, Department of Mathematics, Kobe University)
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April 22(Tue) 15:30--
Jasper STOCKMAN (Univ. of Amsterdam, The Netherlands)
On BC type basic hypergeometric orthogonal polynomials
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April 28(Mon) 15:30--
Maxim NAZAROV (Univ. of York, England)
Capelli identities for the classical Lie algebras
-----------------------------------------------------------------
For further information, contact:
Masatoshi NOUMI
or Masahiko SAITO
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INFINITE ANALYSIS NEWS LETTER No. 251 April 8, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker : Dr. E. Vasserot and Dr. M. Varagnolo
Title : Double loop algebras and their quantization
Abstract: The purpose of the talks is to introduce a quantization of
Lie algebras of currents over a complex 2-dimensional torus.
The main subjects are:
the classical algebras and their presentation,
the quantization and the Schur duality,
the Fock space representation,
the action on the flag variety.
Time & Place: May 6 (Tue) 16:00-17:00 Room 402, RIMS, Kyoto University
May 7 (Wed) 10:30-11:30 Room 009, RIMS, Kyoto University
May 8 (Thu) 10:30-11:30 Room 009, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 250 April 4, 1997
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"Infinite Analysis Lecture Note"
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The following issue is available now.
Contact: juten::kusm.kyoto-u.ac.jp
(No. 15 has not been appeared yet.)
No. 16 @500 yen
"城崎ワークショップ「楕円型 R 行列と可換微分・差分作用素」"
内容：
「可解格子模型の手法による可換差分作用素系の構成」
長谷川浩司述
赤坂立也、浅井良典、松野陽一郎記
「Elliptic colutions of the Yang-Baxter equation」
渋川陽一述
竹村剛一記
「Macdonald 多項式入門」
野海正俊述
中島達洋記
「Capelli identities and generalized hypergeomteric
functions」
大島利雄述
早田孝博記
「Classification of commuting differential operators」
落合啓之述
川向洋之、早田孝博記
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INFINITE ANALYSIS NEWS LETTER No. 249 March 31, 1997
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"Infinite Analysis Lecture Note"
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The following two issues are available now.
Contact: juten::kusm.kyoto-u.ac.jp
No. 13 @1,000 yen
「幾何学的 Langlands program とその周辺」
(Japanese)
執筆者：長谷川浩司、堀田良之、黒木玄、
中島啓、落合啓之、塩田隆比呂、
武部尚志
----------------------------------------
No. 14 @2,000yen
"Infinite Analysis --- Integrable Systems and
Representation Theory --- October 15--19, 1996,
IIAS"
Contents:
(The contributions with * at the end of the title are written
in Japanese.
Toshiki NAKASHIMA, Andrei ZELEVINSKY
Crystal Cone Realization of Quantized Kac-Moody Algebras$^*$
Kaoru IKEDA
The Modified Classical Yang-Baxter Equation and the Algebraic
Groups
Atsuo KUNIBA, Kailash C. MISRA, Masato OKADO, Taichiro TAKAGI,
Jun UCHIYAMA
パスと Demazure 結晶と対称関数*
Akihiro TSUCHIYA, Takeshi SUZUKI, Tomoyuki ARAKAWA
Degenerate Double Affine Hecke Algebra and KZ-equation$^*$
Vitaly TARASOV
Functional model for dynamical elliptic $R$-matrices
Vladimir E. KOREPIN, Takeshi OOTA
Relation between Classical Self-Dual Yang-Mills Equation and
Quantum Inverse Scattering Method
Saburo KAKEI
Orthogonal bases of Calogero-type models
Masatoshi NOUMI
Symmetric and nonsymmetric Macdonald polynomials
Hiraku NAKAJIMA
ジャック多項式と曲面の上の点のヒルベルト概型*
Shigenori YAMANE
Perfect Crystal Of $U_q(G^{(1)}_2)$
Yousuke OHYAMA
Nonlinear equations on theta constants of genus two
Kouichi TAKEMURA, Denis UGLOV
Level-0 action on $U_q(\widehat{\goth{sl}}_{\,n})$
on the $q$-deformed Fock spaces
Kazuyuki OOSHIMA
$C_r$ 型ヤンギアン代数の RRL 定式化への試み$^*$
Atsushi NAKAYASHIKI
On the $sl_N$ Knizhnik-Zamolodchikov Equation on Level 0
Kouichi TAKEMURA, Denis UGLOV
The orthogonal eigenbasis and norms of eigenvectors in the Spin
Calogero-Sutherland Model
Nobuhisa FUKUSHIMA
An algebra arising from 2-state chiral Potts model and Sklyanin
algebra
Masaki KASHIWARA, Tatsuya AKASAKA
Finite-dimensional representations of quantum affine algebras
Jens-U. H. PETERSEN
On a $q$-affine Clifford algebra for the level 1
Fock space of $U_q(\widehat{sl}_n)$
Ruihong YUE, Tetsuo DEGUCHI
Diagonalization of 2-D inhomogeneous model related
to the Hubbard model
Takeo KOJIMA, Vladimir E. KOREPIN
Differential equation for temperature-dependent correlation
function of Delta-interacting Bose gas*
Michio JIMBO, Hitoshi KONNO, Tetsuji MIWA
Degeneration of the Elliptic Algebra ${\cal A}_{q,p}
(\widehat{sl}_2)$: Application to Massless XXZ Model
Yoshihisa SAITO
Quantum toroidal algebras and their vertex representations
Yoshiyuki KOGA
Vertex operators related with the spin representation
of $U_q(D^{(1)}_n)$
Michitomo NISHIZAWA, Kimio UENO
Integral solutions of $q$-difference equations of the
hypergeometric type with $|q|=1$
Tatsuya UENO
Two-toroidal Lie algebra and Four-dimensional K\"ahler WZW Model
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INFINITE ANALYSIS NEWS LETTER No. 248 March 10, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Dr. Stanislav Pakuliak
(Bogoliubov Lab. for Theoretical Phys.)
Title : Algebraic structure of the massless XXZ model (tentative)
Time : March 12(Wed), 13(Thu), 14(Fri), 10:00-12:00 a.m.
Place : Room 115, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 247 February 5, 1997
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Seminar Information
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Surveys in Geometry "サイバーグ・ウィッテン理論"
日時：３月17日(月)から21日(金)
場所：京都大学数理解析研究所
プログラム
１７日
１２：００ー１３：００深谷１
１３：３０ー１５：００古田
１５：３０ー１７：００午腸
１８日
１０：００ー１２：００古田
１３：３０ー１５：００午腸
１５：３０ー１７：００小野
１９日
１０：００ー１２：００古田
１３：３０ー１５：３０深谷２
２０日
１０：００ー１２：００古田
１３：３０ー１５：００深谷２
１５：３０ー１７：００亀谷
２１日
１０：００ー１２：００古田
１３：３０ー１５：００深谷２
参加を希望する大学院生に対して，旅費の補助をできる可能性があります．
希望者は深谷まで電子メールまたは郵便でご連絡下さい．３月１日を締め切りに
します．
連絡先：
深谷賢治：京都大学大学院理学研究科数学教室，京都市左京区北白川追分町
講演者・タイトルなど（講演順）：
深谷賢治１（京大理学部）
サイバーグウィッテン理論要約
「余り予備知識が無い参加者を念頭に，あとの講演を聞くための最低限の要約を
話す．（数学の部分だけ）多少とも予備知識がある人は，聞く必要がないと思われ
る．」
古田幹雄氏（京大数理研）
Seiberg-Witten理論と双対性
「４次元 N=2 超対称 Yang-Mills 理論の低エネルギー有効作用に関する
Seiberg-Witten理論」の「非専門家による非専門家むけの解説」を目標とする。
物理の予備知識は仮定しない。
量子効果とは何か、の説明からはじめる。
午腸徹氏（東京大学数理科学研究科）
Super Symmetry 入門
小野薫氏（お茶の水大学理学部）
Symplectic 多様体上のモノポール方程式
（タウベスらの仕事の紹介）
深谷賢治２（京大理学部）
数学者による数学者のためのString Duality概説
「超弦理論の双対性にもとずくここ２・３年間の進展について，講演者の分かる
範囲で，数学者向けに解説することを目標とする．超弦理論についての予備知識
は仮定しない．超弦理論とそのEffective Field theory, ＴおよびＳ双対，
String String Duality，M理論，F理論，D-braneなど」
亀谷幸夫氏（佐賀大学理工学部）
サイバーグウィッテン不変量とドナルドソン不変量
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INFINITE ANALYSIS NEWS LETTER No. 246 February 4, 1997
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Seminar Information
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Lectures
Speaker: Professor T. Eguchi (The University of Tokyo)
Title : Developments in String Duality
Time : February 18 (Tue)
10:30-12:00 16:00-17:30 (Room 402)
February 19 (Wed)
10:30-12:00 13:30-15:00 (Room 102)
Place : RIMS, Kyoto University
[Professor Eguchi reviews recent developments in string duality.
He also discusses their implications on supersymmetric field
theories.]
----- This is the second and final announcement of this
lecture. There has been no change of detail
from the first announcement, posted in November. -----
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INFINITE ANALYSIS NEWS LETTER No. 245 January 31, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor M. Nazarov (York University)
Title :
1. Zeroes of quantum L-operators and generalized Capelli identities.
The general linear case.
2. Zeroes of quantum L-operators and generalized Capelli identities.
The case of symplectic and orthogonal Lie algebras.
3. Zeroes of quantum L-operators and generalized Capelli identities.
The queer Lie superalgebra case.
Time : April 11 (Fri), 18 (Fri), 25 (Fri), 12:00-13:00
Place: Room 102, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 244 January 30, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor Harvey Segur (Colorado)
Title : Waves in shallow water
Abstract: This talk reviews work done in a joint theoretical-
experimental program to develop an accurate, useful model of
waves in shallow water. Here are our main results.
(a) Laboratory experiments show the existence of waves of finite
amplitude, which propagate with nearly permanent form in shallow water of
uniform depth. The surface patterns of these waves are two-dimensional and
periodic.
(b) These waves are described with reasonable accuracy by a family of
exact solutions of the Kadomtsev-Peviashvili equation, a nonlinear
partial differential equation in 2(space)+1(time) dimensions, which is
completely integrable.
(c) Large-amplitude oceanic waves sometimes arrange themeselves into
similar patterns (i.e., travelling waves of nearly permanent form, with
two-dimensional, periodic surface patterns). This self-orgnized pattern
can dictate features of the waves, including their "groupiness".
Time: February 10 (Mon), 14:00-15:00
Place: Room 115, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 243 January 29, 1997
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Seminar Information
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Seminar on Geometry and Mathematical Physics
Time : Monday, February 3, 15:00 - 16:30
Place : Department of Mathematical Sciences, University of Tokyo
Komaba Campus Room 128
Speaker: Hiraku Nakajima (University of Tokyo)
Title : 3次元 N=4 超対称 Yang-Mills gauge理論と3次元多様体の有限型不変量
(after Seiberg-Witten, Rozansky-Witten, etc...)
------------------------------------------------
For more information, please point your www client at
http://mint.ms.u-tokyo.ac.jp/GeomPhys.html
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Toshitake Kohno, Toru Gocho
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INFINITE ANALYSIS NEWS LETTER No. 242 January 28, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor Denis Uglov (RIMS)
Title : Yangian Gelfand-Zetlin bases, gl(N)-Jack Polynomials
and Dynamical Correlation Functions
in the Spin Calogero-Sutherland Model.
Date : January 31 (Fri), 12:00--13:00
Place : Room 102, RIMS, Kyoto University
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INFINITE ANALYSIS NEWS LETTER No. 241 January 24, 1997
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Seminar Information
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Infinite Analysis Seminar
Speaker: Professor Seok-Jin Kang
(Seoul National University)
Title : Graded Lie superalgebra and superdimension formula
Date : February 7 (Fri), 12:00--13:00
Place : Room 102, RIMS, Kyoto University
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