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DUNKL OPERATORS FOR COMPLEX REFLECTION GROUPS

Published online by Cambridge University Press:  28 January 2003

C. F. DUNKL  and
E. M. OPDAM
C. F. DUNKL
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904-4137, USA. [email protected]
E. M. OPDAM
Affiliation:
Korteweg de Vries Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018TV Amsterdam, The Netherlands. [email protected]
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Abstract

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.

2000 Mathematical Subject Classification: 20F55 (primary), 52C35, 05E05, 33C08 (secondary).

Keywords

complex reflection groupDunkl operatorrational Cherednik algebra
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 86 , Issue 1 , January 2003 , pp. 70 - 108
Copyright
2003 London Mathematical Society

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