Abstract: this is a joint work with Roman Travkin. A conjecture of Davide Gaiotto predicts that the category of representations of quantum supergroup U_q(gl(M|N)) can be realized as a category of twisted D-modules with certain equivariant condition on the affine Grassmannian Gr_N. The untwisted version of the above conjecture says that the category of representations of the degenerate supergroup is equivalent to  the category of (non-twisted) D-modules, with the same equivariant condition on Gr_N. In the case of M=N-1 and M=N, the latter was proved by A. Braverman, M. Finkelberg, V. Ginzburg, and R. Travkin. In this paper, we proved all other cases.

Also, we prove that we can realize the category of representations of the degenerate supergroup as a category of D-modules on the mirabolic subgroup Mir_L(F) with certain equivariant conditions for any L bigger than N and M.