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Dunkl operators for complex reflection groups
- Source :
- Proceedings of the London Mathematical Society, (3) 86(1), 70-108. Oxford University Press
- Publication Year :
- 2001
- Publisher :
- arXiv, 2001.
-
Abstract
- Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parametrized 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 parameter family of these structures is described explicitly, using the theory of nonsymmetric Jack polynomials.<br />Comment: 36 pages; Programme on Symmetric Functions and Macdonald Polynomials at the Isaac Newton Institute
- Subjects :
- Double affine Hecke algebra
Polynomial
52C35, 05E05, 33C08 (Secondary)
010308 nuclear & particles physics
General Mathematics
Polynomial ring
010102 general mathematics
01 natural sciences
20F55 (Primary)
Algebra
Set (abstract data type)
Reflection (mathematics)
Mathematics::Quantum Algebra
0103 physical sciences
Covariance and contravariance of vectors
FOS: Mathematics
0101 mathematics
Parametric family
Representation Theory (math.RT)
Mathematics::Representation Theory
Mathematics - Representation Theory
Mathematics
Dunkl operator
Subjects
Details
- ISSN :
- 00246115
- Database :
- OpenAIRE
- Journal :
- Proceedings of the London Mathematical Society, (3) 86(1), 70-108. Oxford University Press
- Accession number :
- edsair.doi.dedup.....b5c9ab109751e497e71e0816c43d6591
- Full Text :
- https://doi.org/10.48550/arxiv.math/0108185