Untwisted Gaiotto equivalence

Abstract

This is a successive paper of arXiv:1909.11492. We prove an equivalence between the category of finite-dimensional representations of degenerate supergroup $\underline{GL}(M|N)$ and the category of $(G{L}_M(O)⋉U_{M,N}(F),{\chi }_{M,N})$-equivariant D-modules on $G{r}_N$. We also prove that we can realize the category of finite-dimensional representations of degenerate supergroup $\underline{GL}(M|N)$ as a category of D-modules on the mirabolic subgroup $Mi{r}_L(F)$ with certain equivariant conditions for any $L$ bigger than $N$ and $M$.

40 pages, published version, add acknowledgements and references