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Dunkl Operators for Complex Reflection Groups
Author(s) -
Dunkl C. F.,
Opdam E. M.
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013825
Subject(s) - mathematics , parameterized complexity , reflection (computer programming) , covariance and contravariance of vectors , ring (chemistry) , pure mathematics , polynomial , algebra over a field , polynomial ring , group (periodic table) , combinatorics , mathematical analysis , computer science , chemistry , organic chemistry , programming language
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).
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