Moduli Spaces of Sheaves on Surfaces: Hecke Correspondences and Representation Theory

Abstract

We construct explicit elements W k ij in (a completion of) the shifted quantum toroidal algebra of type A, and show that these elements act by 0 on the K-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements W k ij will be related to q-deformed W -algebras of type A for arbitrary nilpotent, which would imply a q-deformed version of the AGT correspondence between gauge theory with surface operators and conformal field theory.Proposition 4.5. Under the action of Theorem 4.3, the elements (2.21) act on K r as the operators (4.7) with the same name, hence the abuse of notation.