arXiv subjects
Publications and source records attributed to Ruotao Yang.
This paper is a part of the series proving the Gaiotto conjecture for basic classical quantum supergroups. The previous part arXiv:2107.02653 [math.RT] , arXiv:2306.09556 [math.RT], proved the Gaiotto conjecture for the general linear quantum supergroups $U_q(\mathfrak{gl}(N|M))$. Here we deal with the exceptional quantum supergroup $U_q(\mathfrak{f}(4))$.
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.
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 $(GL_M(O) \ltimes U_{M, N}(F), \chi_{M, N})$-equivariant D-modules on $Gr_{N}$. 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 $Mir_L(F)$ with certain equivariant conditions for any $L$ bigger than $N$ and $M$.
This paper considers a tiny modification of Justin Campbell's construction of the Kontsevich compactification in arXiv:1606.01518 [math.AG]. We construct a resolution of singularities of Drinfeld compactification with an Iwahori structure and use it to prove the universally local acyclity of !-extension D-module on the Drinfeld compactification with an Iwahori structure.
We prove the twisted Whittaker category on the affine flag variety and the category of representations of the mixed quantum group are equivalent. In particular, we prove that the quantum category O is equivalent to the category of twisted Whittaker D-modules on affine flags in the generic case.
Let G be a connected reductive group over an algebraic closure of a finite field Fq. In this paper it is proved that the infinite dimensional Steinberg module of kG defined by N. Xi in 2014 is irreducible when k is a field of positive characteristic and char k is not char Fq. For certain special linear groups, we show that the Steinberg modules of the groups are not quasi-finite with respect to some natural quasi-finite sequences of the groups.