Yasushi Komori, Masatoshi Noumi, Jun'ichi Shiraishi, “Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications”, SIGMA, 2009, Volume 5,054, 40 pp.

This article is cited in 36 papers

Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications

Yasushi Komori^a, Masatoshi Noumi^b, 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

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.

Keywords: kernel function; Ruijsenaars operator; Koornwinder polynomial.

MSC: 81R12; 33D67

Received: December 1, 2008; in final form April 30, 2009; Published online May 12, 2009

Language: English

DOI: 10.3842/SIGMA.2009.054