Hecke correspondences for smooth moduli spaces of sheaves

Abstract

Abstract We define functors on the derived category of the moduli space ℳ of stable sheaves on a smooth projective surface (under Assumptions A and S below), and prove that these functors satisfy certain commutation relations. These relations allow us to prove that the given functors induce an action of the elliptic Hall algebra on the

K

$K$ -theory of the moduli space ℳ, thus generalizing the action studied by Nakajima, Grojnowski and Baranovsky in cohomology.