Finite dimensional representations of symplectic reflection algebras associated to wreath products

Details Finite dimensional representations of symplectic reflection algebras associated to wreath products Finite dimensional representations of symplectic reflection algebras associated to wreath products

2004-03-15

arxiv.org/abs/math/0403250v2

Mathematics

Representation Theory

10 pages, latex

Scientific paper

In this paper we construct finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a number and c a class function on the set of nontrivial elements of G). Specifically, we show that if W is an irreducible representation of S_N whose Young diagram is a rectangle, and Y an irreduible finite dimensional representation of H(c,1,G), then the representation M=W\otimes Y^N of H(0,c_0,N,G) can be deformed along a hyperplane in the space of parameters (k,c) passing through c_0. On the other hand, if Y is 1-dimensional and the Young diagram of W is not a rectangle, such a deformation does not exist.

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