Dunkl operators for complex reflection groups

• Autores: C. F. Dunkl, E. M. Opdam
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 86, Nº 1, 2003, págs. 70-108
• Idioma: inglés
• DOI: 10.1112/s0024611502013825
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• Resumen

  • 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.