  In $\rm{GL}_N$, a series of subgroups indexed by $0\leq M\leq N-1$ were
noticed by H. Jacquet-I. Piatetski Shapiro-J. Shalika, J. Cogdell, and D.
Gaiotto. It was conjectured by D. Gaiotto that the categories of twisted
D-modules on the affine Grassmannian of $\rm{GL}_N$ with equivariant structure
with respect to these subgroups are equivalent to the categories of
representations of quantum supergroups $U_q(\mathfrak{gl}(M|N))$. When $M=0$
and $M=N-1$, this conjecture was proved due to D. Gaitsgory and A. Braverman-M.
Finkelberg-R. Travkin, respectively. In this paper, we prove the other cases.
  We adapt the global method originating from arXiv:math/0611323 and
arXiv:0705.4571. In order to compare the global definition of Gaiotto category
with the local definition, we generalize the local-global comparison theorem of
arXiv:1811.02468 to a general setting.
