The McKay correspondence for finite subgroups of SL(3,C)

Let G subset of SL(n, C) be a finite subgroup and phi: Y --> X = C-n/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime divisors of Y correspond one-to-one with ''junior'' conjugacy classes of G. When n = 2 this is a version of the McKay correspondence (with irreducible representations of G replaced by conjugacy classes). In the case n = 3, a resolution with K-Y = 0 is known to exist by work of Roan and others; we prove the existence of a basis of H*(Y, Q) by algebraic cycles in one-to-one correspondence with conjugacy classes of G. Our treatment leaves lots of open problems.