Dunkl operators for complex reflection groups
Representation Theory
2007-05-23 v1
Abstract
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.
Cite
@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}
}
Comments
36 pages; Programme on Symmetric Functions and Macdonald Polynomials at the Isaac Newton Institute