Kernel identities for van Diejen's $q$-difference operators and transformation formulas for multiple basic hypergeometric series

Abstract

In this paper, we show that the kernel function of Cauchy type for type $BC$ intertwines the commuting family of van Diejen's $q$-difference operators. This result gives rise to a transformation formula for certain multiple basic hypergeometric series of type $BC$. We also construct a new infinite family of commuting $q$-difference operators for which the Koornwinder polynomials are joint eigenfunctions.

29 pages. Typos corrected. Subsection 4.3 is modified

References in corpus (3)

• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
• An (inverse) Pieri formula for Macdonald polynomials of type C
• Karlsson-Minton type hypergeometric functions on the root system C_n