Related papers: Mirabolic Satake equivalence and supergroups

We study the semisimplification of the full karoubian subcategory generated by the irreducible finite dimensional representations of the algebraic supergroup $GL(m|n)$ over an algebraically closed field of characteristic zero. This…

We introduce various affine Grassmannians, study their geometric properties, and give some applications. We also discuss the geometric Satake equivalence. These are the expanded lecture notes for a mini-course in 2015 PCMI summer school.…

We give an explicit combinatorial description of the category Perv(S,N) of perverse sheaves on an oriented surface S (with boundary) with singularities at a given finite set N. The description is given in terms of any spanning graph K in S…

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the…

We construct an equivalence of graded Abelian categories from a category of representations of the quiver-Hecke algebra of type $A_1^{(1)}$ to the category of equivariant perverse coherent sheaves on the nilpotent cone of type $A$. We prove…

We give an exposition of three geometric constructions of the irreducible representations of GL_n. In particular, we discuss Borel-Weil theory, the Ginzburg construction, and the geometric Satake construction. We also explain how to deduce…

We show that tilting modules and parity sheaves on the affine Grassmannian are related through the geometric Satake correspondence, when the characteristic is bigger than an explicit bound.

Perverse schobers are conjectural categorical analogs of perverse sheaves. We show that such structures appear naturally in Homological Minimal Model Program which studies the effect of birational transformations such as flops, on the…

In this paper we extend the twisted Satake equivalence established in arXiv:0809.3738 for almost simple groups to the case of split reductive groups.

We show that the mirabolic quantum group $MU(n)$ is a comodule algebra over the quantized enveloping algebra $U_v(\mathfrak{sl}_n)$, and use this structure to give a complete classification of its finite dimensional representations. In…

We identify equivariant quasicoherent sheaves on the Grothendieck alteration of a reductive group $\mathsf{G}$ with universal monodromic Iwahori--Whittaker sheaves on the enhanced affine flag variety of the Langlands dual group $G$. This…

We show that quasi-projective relation algebras and directed cylindric algebras are equivalent categorialy. We work out a Godels second incompleteness theorem for finite varibale fragments of first order logic. We show that distinct set…

For the group GL(n), we construct an action of the equivariant derived category of coherent sheaves on the Grothendieck-Springer resolution on a certain subcategory of a finite monodromic Hecke category. We use this to construct a partial…

Fargues and Scholze proved the geometric Satake equivalence over the Fargues--Fontaine curve. On the other hand, Zhu proved the geometric Satake equivalence using a Witt vector affine Grassmannian. In this paper, we explain the relation…

We study geometric representation theory of Lie algebroids. A new equivalence relation for integrable Lie algebroids is introduced and investigated. It is shown that two equivalent Lie algebroids have equivalent categories of infinitesimal…

Inspired by the works of Rickard on splendid equivalences and of Chuang and Rouquier on perverse equivalences, we are here interested in the combination of both, a splendid perverse equivalence. This is naturally the right framework to…

We study a category of Iwahori-equivariant modular perverse sheaves on some avatar of the semi-infinite flag variety, by adapting the work of Arkhipov-Bezrukavnikov-Braverman-Gaitsgory-Mirkovi\'c. We then construct a functor between the…

We introduce and study certain hyperbolic versions of automorphic Lie algebras related to the modular group. Let $\Gamma$ be a finite index subgroup of $\mathrm{SL}(2,\mathbb{Z})$ with an action on a complex simple Lie algebra $\mathfrak…

We lay the foundations for the study of relatively quasiconvex subgroups of relatively hyperbolic groups. These foundations require that we first work out a coherent theory of countable relatively hyperbolic groups (not necessarily finitely…

We give a description of certain categories of equivariant coherent sheaves on Grothendieck's resolution in terms of the categorical affine Hecke algebra of Soergel. As an application, we deduce a relationship of these coherent sheaf…