Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 054, 40 pages      arXiv:0812.0279      https://doi.org/10.3842/SIGMA.2009.054
Contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions”

Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications

Yasushi Komori a, Masatoshi Noumi b and Jun'ichi Shiraishi c
a) Graduate School of Mathematics, Nagoya University, Chikusa-Ku, Nagoya 464-8602, Japan
b) Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
c) Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan

Received December 01, 2008, in final form April 30, 2009; Published online May 12, 2009

Abstract
A unified approach is given to kernel functions which intertwine Ruijsenaars difference operators of type A and of type BC. As an application of the trigonometric cases, new explicit formulas for Koornwinder polynomials attached to single columns and single rows are derived.

Key words: kernel function; Ruijsenaars operator; Koornwinder polynomial.

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