Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves

We define complexes of vector bundles on products of moduli spaces of framed rank r torsion-free sheaves on the complex projective plane. The top non-vanishing Chern classes of the cohomology of these complexes yield actions of the r-colored Heisenberg and Clifford algebras on the equivariant cohomology of the moduli spaces. In this way we obtain a geometric realization of the boson-fermion correspondence and related vertex operators.