Multivariable Wilson polynomials and degenerate Hecke algebras

被引：0
作者：
Wolter Groenevelt
机构：
[1] Technische Universiteit Delft,Delft Institute of Applied Mathematics
来源：
Selecta Mathematica | 2009年 / 15卷
关键词：
Primary 33C52; 33C80; Secondary 20C08;
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摘要：
We study a rational version of the double affine Hecke algebra associated to the nonreduced affine root system of type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(C^\vee_{n}, C_{n})}$$\end{document} . A certain representation in terms of difference-reflection operators naturally leads to the definition of nonsymmetric versions of the multivariable Wilson polynomials. Using the degenerate Hecke algebra we derive several properties, such as orthogonality relations and quadratic norms, for the nonsymmetric and symmetric multivariable Wilson polynomials.
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