  For a class of K3 surfaces, the action of a Lie algebra which is a certain
affinization of a Kac-Moody algebra is given on the cohomology of the moduli
spaces of rank 1 torsion free sheaves on the surface. This action is generated
by correspondences between moduli spaces of Bridgeland stable objects on the
surface, and is equivalent to an action defined using Fourier coefficients of
vertex operators. Two other results are included: a more general result giving
geometric finite dimensional Lie algebra actions on moduli spaces of Bridgeland
stable objects on K3 surfaces subject to natural conditions and a geometric
modular interpretation of some quiver varieties for affine ADE quivers.
