Framed torsion-free sheaves on CP2, Hilbert schemes, and representations of infinite dimensional Lie algebras

We construct representations of both Heiseberg and Clifford algebras on the equivariant cohomology of the moduli space of framed torsion-free sheaves on P2, as well as on the equivariant cohomology of the Hilbert scheme of points on the resolution of a type A simple singularity. This generalizes the earlier work of Nakajima, Grojnowski, and others.