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.