Ju l 2 00 6 Framed Rank r Torsion - free Sheaves on C P 2 and Representations of the Affine Lie

We construct geometric realizations of the r-colored bosonic and fermionic Fock space on the equivariant cohomology of the moduli space of framed rank r torsion-free sheaves on CP 2. Using these constructions, we realize geometrically all level one irreducible representations of the affine Lie algebra gl(r). The cyclic group Z k acts naturally on the moduli space of sheaves, and the fixed-point components of this action are cyclic Nakajima quiver varieties. We realize level k irreducible representations of gl(r) on the equivariant cohomology of these quiver varieties.