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

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