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 arXiv:math/0702670 and arXiv:0801.1530 respectively.