An action of a Lie algebra on the homology groups of moduli spaces of stable sheaves

Abstract

We construct an action of a Lie algebra on the homology groups of moduli spaces of stable sheaves on K3 surfaces under some technical conditions. This is a generalization of Nakajima's construction of sl_2-action on the homology groups. In particular, for an A,D,E-configulation of (-2)-curves, we shall give a collection of moduli spaces such that the associated Lie algebra acts on their homology groups.