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

TL;DR

This paper constructs geometric actions of algebraic structures on moduli spaces of framed torsion-free sheaves, providing a geometric realization of vertex operators and the boson-fermion correspondence.

Contribution

It introduces complexes of vector bundles on moduli spaces that realize Heisenberg and Clifford algebra actions via Chern classes, linking geometry with algebraic structures.

Findings

Realization of algebra actions on cohomology

Connection between geometry and vertex operators

Geometric interpretation of boson-fermion correspondence

Abstract

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.