Singular Polynomials for the Symmetric Group and Krawtchouk Polynomials
量子代数
2007-05-23 v1 经典分析与常微分方程
摘要
A singular polynomial is one which is annihilated by all Dunkl operators for a certain parameter value. These polynomials were first studied by Dunkl, de Jeu and Opdam, (Trans. Amer. Math. Soc. 346 (1994), 237-256). This paper constructs a family of such polynomials associated to the irreducible representation (N-2,1,1) of the symmetric group S_N for odd N and parameter values -1/2, -3/2, -5/2,... . The method depends on the use of Krawtchouk polynomials to carry out a change of variables in a generating function involved in the construction of nonsymmetric Jack polynomials labeled by (m,n,0,....), m>=n.
引用
@article{arxiv.math/0310249,
title = {Singular Polynomials for the Symmetric Group and Krawtchouk Polynomials},
author = {Charles F. Dunkl},
journal= {arXiv preprint arXiv:math/0310249},
year = {2007}
}
备注
submitted to Proceedings of 10th Kravchuk International Conference (2004), 12 pages