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INFINITE ANALYSIS NEWS LETTER  No. 255  May 19, 1997
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Secretariat, Juten Ryoiki Kenkyu 231
Tel. & Fax: 075-753-3707 Email: juten::kusm.kyoto-u.ac.jp

We welcome related information.
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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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