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 $\mathfrak{sl}_2$-action on the homology groups [N6]. In particular, for an $A$, $D$, $E$-type configulation of $(-2)$-curves, we shall give a collection of moduli spaces such that the associated Lie algebra acts on their homology groups.