  Kirillov has described a McKay correspondence for finite subgroups of
PSL_{2}(C) that associates to each `height' function an affine Dynkin quiver
together with a derived equivalence between equivariant sheaves on the
projective line P^1 and representations of this quiver. The equivalences for
different height functions are then related by reflection functors for quiver
representations.
  The main goal of this paper is to develop an analogous story for the
cotangent bundle of P^1. We show that each height function gives rise to a
derived equivalence between equivariant sheaves on the cotangent bundle T*P^1
and modules over the preprojective algebra of an affine Dynkin quiver. These
different equivalences are related by spherical twists, which take the place of
the reflection functors for P^1.
