Morita equivalence problem for symplectic reflection algebras

In this paper we fully solve the Morita equivalence problem for symplectic reflection algebras associated to direct products of finite subgroups of SL₂ (C). Namely, given a pair of such symplectic reflection algebras Hc, H₂', then Hc is Morita equivalent to Hc' 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.