On elliptic Dunkl operators
Quantum Algebra
2007-06-15 v1 Representation Theory
Abstract
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.
Cite
@article{arxiv.0706.2152,
title = {On elliptic Dunkl operators},
author = {Pavel Etingof and Xiaoguang Ma},
journal= {arXiv preprint arXiv:0706.2152},
year = {2007}
}