Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

Abstract

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras associated with wreath-products.

Cite this paper

@inproceedings{Etingof2005HarishChandraHA, title={Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products}, author={Pavel Etingof and Wee Liang Gan and Victor Ginzburg and Alexei Oblomkov}, year={2005} }