Morita equivalence problem for symplectic reflection algebras

Abstract

In this paper we fully solve the Morita equivalence problem for symplectic reflection algebras associated to direct products of finite subgroups of $S{L}_2(\mathbb{C})$. Namely, given a pair of such symplectic reflection algebras $H_c,H_{c^{\prime }}$,then $H_c$ is Morita equivalent to $H_c^{\prime }$ if and only if they are related by a standard Morita equivalence. We also establish new cases for Morita classification problem for type A rational Cherednik algebras. Our approach crucially relies on the reduction modulo large primes.

14 pages, preliminary version, all comments welcome