Dunkl operators for complex reflection groups
表示论
2007-05-23 v1
摘要
Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parametrized family of deformations of the polynomial De Rham complex. This leads to the study of the polynomial ring as a module over the "rational Cherednik algebra", and a natural contravariant form on this module. In the case of the imprimitive complex reflection groups G(m,p,N), the set of singular parameters in the parameter family of these structures is described explicitly, using the theory of nonsymmetric Jack polynomials.
引用
@article{arxiv.math/0108185,
title = {Dunkl operators for complex reflection groups},
author = {C. F. Dunkl and E. M. Opdam},
journal= {arXiv preprint arXiv:math/0108185},
year = {2007}
}
评论
36 pages; Programme on Symmetric Functions and Macdonald Polynomials at the Isaac Newton Institute