Dunkl operators for complex reflection groups

Details Dunkl operators for complex reflection groups Dunkl operators for complex reflection groups

2001-08-28

arxiv.org/abs/math/0108185v1

Proc. London Math. Soc.(3) 86 (2003), 70-108

Mathematics

Representation Theory

36 pages; Programme on Symmetric Functions and Macdonald Polynomials at the Isaac Newton Institute

Scientific paper

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.

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