Affine Laumon spaces and a conjecture of Kuznetsov

Abstract

We prove a conjecture of Kuznetsov stating that the equivariant K-theory of affine Laumon spaces is the universal Verma module for the quantum affine algebra U_q(gl_n^). We do so by reinterpreting the action of the quantum toroidal algebra U_q(gl_n^^) on the K-theory from [14] in terms of the shuffle algebra studied in [12], which constructs an embedding of U_q(gl_n^) into U_q(gl_n^^)

This paper started by breaking up arXiv:1302.6202 into two parts, one geometric and one representation theoretic. The present paper consists of the geometric half, to which we added a number of additional results