On elliptic Dunkl operators

2007/06/14 by Pavel Etingof, Etingof, Pavel, Xiaoguang Ma +1 · 1 citation
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.0706.2152

9 pages, latex

arxiv created 2007/06/14 · arxiv updated 2009/12/01

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.

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• Generic Hecke algebras in the infinite

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• Cherednik and Hecke algebras of varieties with a finite group action
• Representations of the elliptic affine Hecke algebras