On some finite dimensional representations of symplectic reflection algebras associated to wreath products

Details On some finite dimensional representations of symplectic reflection algebras associated to wreath products On some finite dimensional representations of symplectic reflection algebras associated to wreath products

2004-11-12

arxiv.org/abs/math/0411286v2

Mathematics

Representation Theory

15 pages, 5 figures, latex

Scientific paper

Let G be a finite subgroup of SL(2,C). Let S_N#G^N be the wreath product of G by the symmetric group of degree N, acting symplectically on a complex vector space V of dimension 2N, with symplectic basis {x_i, y_i} i=1,...,N. In this paper we classify all the irreducible representations of S_N#G^N that can be extended to a representation of the associated symplectic reflection algebra H(k,c,N,G) (where k is a complex number and c a class function on the non-trivial elements of G) for non-zero values of k and with trivial action of the generators x_i,y_i\in H(k,c,N,G).

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