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

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 $U_q(\widehat{\mathfrak{gl}}_n)$, improv