McKay correspondence for symplectic quotient singularities

Abstract

We consider the quotients $X=V/G$ of a symplectic complex vector space $V$ by a finite subgroup $G\subset Sp(V)$ which admit a smooth crepant resolution $Y\to X$. For such quotients, we prove the homological McKay correspondence conjectured by M. Reid. Namely, we construct a natural basis in the homology space $H_\cdot(Y,\Q)$ whose elements are numbered by the conjugacy classes in the finite group $G$.

28 pages, LaTeX2e; added new references and corrected a proof (of Proposition 4.1)