On Some Finite Dimensional Representations of Symplectic Reflection Algebras Associated to Wreath Products

Abstract

Let Γ _N : = S _N  ⋉ Γ ^N be the wreath product of Γ, a finite subgroup of SL(2,C), by the symmetric group of degree N. In this article we classify all the irreducible representations of S _N  ⋉ Γ ^N that can be extended to a representation of the associated symplectic reflection algebra H _1,k,c (Γ _N ) (where k is a complex number and c a class function on the nontrivial elements of Γ) for nonzero values of k.

Keywords:

• Symplectic reflection algebras
• Wreath products

Mathematics Subject Classification:

• Primary 16G10
• Secondary 16G20

ACKNOWLEDGMENT

I am very grateful to Pavel Etingof for introducing me to the subject and for many useful conversations and comments.

Notes

Communicated by J. Alev.