A difference-integral representation of Koornwinder polynomials
经典分析与常微分方程
2007-05-23 v1 组合数学
量子代数
摘要
We construct new families of (q-) difference and (contour) integral operators having nice actions on Koornwinder's multivariate orthogonal polynomials. We further show that the Koornwinder polynomials can be constructed by suitable sequences of these operators applied to the constant polynomial 1, giving the difference-integral representation of the title. Macdonald's conjectures (as proved by van Diejen and Sahi) for the principal specialization and norm follow immediately, as does a Cauchy-type identity of Mimachi.
引用
@article{arxiv.math/0409437,
title = {A difference-integral representation of Koornwinder polynomials},
author = {Eric M. Rains},
journal= {arXiv preprint arXiv:math/0409437},
year = {2007}
}
备注
15 pages AMSLaTeX. To appear in proceedings of the Workshop on Jack, Hall-Littlewood and Macdonald polynomials (September 2003, ICMS)