Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parameter family of deformations of the polynomial De Rham complex. This leads to the… (More)

Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free… (More)

For certain negative rational numbers κ0, called singular values, and associated with the symmetric group SN on N objects, there exist homogeneous polynomials annihilated by each Dunkl operator when… (More)

There are examples of Calogero-Sutherland models associated to the Weyl groups of type A and B. When exchange terms are added to the Hamiltonians the systems have nonsymmetric eigenfunctions, which… (More)

We study the rational Cherednik algebra Hc of type G(r, 1, n) by means of the Dunkl-Opdam operators introduced in [DuOp] and the generalized Jack polynomials introduced in [Gri]. Our main result is a… (More)

Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik–Dunkl… (More)

In a 1983 paper [M1], I. G. Macdonald introduced his well-known “constant term conjectures.” These conjectures concern a certain polynomial ∆ = ∆(G, k) that is indexed by a semisimple Lie algebra G… (More)

For certain negative rational numbers κ0, called singular values, and associated with the symmetric group SN on N objects, there exist homogeneous polynomials annihilated by each Dunkl operator when… (More)