Related papers: Hecke category actions via Smith-Treumann theory

The cohomology theory TMF of topological modular forms is a derived algebro-geometric interpretation of the classical ring of complex modular forms from number theory. In this article, we refine the classical Adams operations, Hecke…

We construct reflection functors for quiver Hecke algebras associated with arbitrary symmetrizable Kac-Moody algebras, from a higher representation-theoretic viewpoint. These functors provide a categorification of Lusztig's braid group…

Let G be a reductive group (over an algebraically closed field) equipped with the metaplectic data. In this paper we study the corresponding twisted Whittaker category for G. We construct and study a functor from the latter category to the…

We introduce the notion of a Hamiltonian action of an \'etale Lie group stack on an \'etale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer-Marsden-Weinstein symplectic reduction theorem, and the…

In this paper we construct the action of Ding-Iohara and shuffle algebras in the sum of localized equivariant K-groups of Hilbert schemes of points on C^2. We show that commutative elements K_i of shuffle algebra act through vertex…

We show that the Whittaker functor on a regular block of the BGG-category $\mathcal{O}$ of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with Soergel and Mili\v{c}i\'{c}'s equivalence…

We prove the plectic conjecture of Nekov\'a\v{r}-Scholl over global function fields $Q$. For example, when the cocharacter is defined over $Q$ and the structure group is a Weil restriction from a geometric degree $d$ separable extension…

We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$-action has been considered on a strongly monotone skew-product semiflow. Here we relax the…

Given a finite subgroup G of SL(2,C) we define an additive 2-category H^G whose Grothendieck group is isomorphic to an integral form of the Heisenberg algebra. We construct an action of H^G on derived categories of coherent sheaves on…

We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…

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…

In this paper we construct an abelian category of "mixed perverse sheaves" attached to any realization of a Coxeter group, in terms of the associated Elias-Williamson diagrammatic category. This construction extends previous work of the…

We construct modular categories from Hecke algebras at roots of unity. For a special choice of the framing parameter, we recover the Reshetikhin-Turaev invariants of closed 3-manifolds constructed from the quantum groups U_q sl(N) by…

We study the cohomology of Deligne-Lusztig varieties with aim the construction of actions of Hecke algebras on such cohomologies, as predicted by the conjectures of Brou\'{e}, Malle and Michel ultimately aimed at providing an explicit…

We use categorification of monoid actions to study algebraic geometry over symmetric monoidal categories. This brings together the relative algebraic geometry over symmetric monoidal categories developed by To\"{e}n and Vaqui\'{e}, along…

We study the equivariant oriented cohomology ring $h_T(G/P)$ of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and then prove that the respective Bott-Samelson classes in…

Let $(W, I)$ be a finite Coxeter group. In the case where $W$ is a Weyl group, Berenstein and Kazhdan in \cite{BK} constructed a monoid structure on the set of all subsets of $I$ using unipotent $\chi$-linear bicrystals. In this paper, we…

By a result of Gerstenhaber and Schack the simplicial cohomology ring $H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$, where the poset…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

We attempt to give a gentle (though ahistorical) introduction to Koszul duality phenomena for the Hecke category, focusing on the form of this duality studied in joint work of Achar, Riche, Williamson, and the author. We illustrate some key…