  The quotient of a finite-dimensional vector space by the action of a finite
subgroup of automorphisms is usually a singular variety. Under appropriate
assumptions, the McKay correspondence relates the geometry of nice resolutions
of singularities and the representations of the group. For the Hilbert scheme
of points on the affine plane, we study how different correspondences (McKay,
dual McKay and multiplicative McKay) are related to each other.
