Representations of the Heisenberg algebra and moduli spaces of framed sheaves

TL;DR

This paper constructs a geometric representation of the Heisenberg algebra on the homology of moduli spaces of framed sheaves, extending Nakajima's work on Hilbert schemes of points.

Contribution

It generalizes Nakajima's construction by providing a geometric action of the Heisenberg algebra on moduli spaces of framed torsion free sheaves.

Findings

Established a Heisenberg algebra action on homology of moduli spaces

Extended Nakajima's construction beyond Hilbert schemes

Provided geometric insights into moduli space structures

Abstract

We give a `geometrical' construction of an action of a Heisenberg algebra on the homology of the moduli spaces of torsion free sheaves on a complex smooth connected projective surface, framed along a smooth connected genus zero curve. This result generalizes Nakajima's construction for the Hilbert schemes of points.