Affine Laumon space and contragredient dual Verma module of $U_q({\widehat{\mathfrak{gl}}}_n)$

Abstract

We study the action of the quantum group $U_q({\widehat{\mathfrak{gl}}}_n)$ on the equivariant K-theory of affine Laumon spaces. We show that, at any lowest weight away from the critical level, this can be identified with the contragredient dual Verma module of $U_q({\widehat{\mathfrak{gl}}}_n)$, improving earlier results of Braverman-Finkelberg and Neguţ. The proof uses a variant of stable envelopes first introduced by Maulik-Okounkov in the study of Nakajima quiver varieties.

Expanded some proofs and fixed some typos