Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
Yasushi Komori, Masatoshi Noumi, Jun'ichi Shiraishi
TL;DR
This paper develops a unified framework for kernel functions that connect Ruijsenaars difference operators of types A and BC, leading to new explicit formulas for Koornwinder polynomials in specific cases.
Contribution
It introduces a unified approach to kernel functions for Ruijsenaars difference operators and derives new explicit formulas for Koornwinder polynomials.
Findings
Unified kernel functions for types A and BC operators
Explicit formulas for Koornwinder polynomials for single columns and rows
Enhanced understanding of Ruijsenaars difference operators
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.
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