Representations of Gan–Ginzburg algebras

Abstract

Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan–Ginzburg algebra of rank n. When the quiver is affine Dynkin, we obtain an explicit construction of representations of the corresponding wreath product symplectic reflection algebra of rank n. When the quiver is star-shaped, but not finite Dynkin, we use this functor to obtain a Lie-theoretic construction of representations of a “spherical” subalgebra of the Gan–Ginzburg algebra isomorphic to a rational generalized double affine Hecke algebra of rank n. Our functors are a generalization of the type A and type BC functors from [1] and [4], respectively.