On elliptic Dunkl operators

Details On elliptic Dunkl operators On elliptic Dunkl operators

2007-06-14

arxiv.org/abs/0706.2152v1

Mathematics

Quantum Algebra

9 pages, latex

Scientific paper

We attach elliptic Dunkl operators to an abelian variety with a finite group action. This generalizes elliptic Dunkl operators for Weyl groups, defined by Buchstaber, Felder, and Veselov in 1994. We show that these operators commute, and use them to define representations from category O of elliptic Cherednik algebras. We also consider the monodromy representations of differential equations defined by elliptic Dunkl operators, and show that they yield finite dimensional rrepresentations of generalized double affine Hecke algebras.

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