McKay correspondence for symplectic quotient singularities

We consider the quotients $X=V\mathrm{/}G$ 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 $H_{\cdot }(Y,\text{Q})$ whose elements are numbered by the conjugacy classes in the finite group $G$.