Resumen de Dunkl operators for complex reflection groups

C. F. Dunkl, E. M. Opdam

• Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parameterized 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 parameterized family of these structures is described explicitly, using the theory of non-symmetric Jack polynomials.