Deformed preprojective algebras and symplectic reflection algebras for wreath products

Abstract

We determine the PBW deformations of the wreath product of a symmetric group with a deformed preprojective algebra of an affine Dynkin quiver. In particular, we show that there is precisely one parameter which does not come from deformation of the preprojective algebra. We prove that the PBW deformation is Morita equivalent to a corresponding symplectic reflection algebra for wreath product.