Related papers: On the affine Hecke category for $SL_3$

We give a cohomological classification of vector bundles of rank $2$ on a smooth affine threefold over an algebraically closed field having characteristic unequal to $2$. As a consequence we deduce that cancellation holds for rank $2$…

We define an exact functor $F_{n,k}$ from the category of Harish-Chandra modules for $GL(n,R)$ to the category of finite-dimensional representations for the degenerate affine Hecke algebra for $gl(k)$. Under certain natural hypotheses, we…

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…

The set HLie(n) of the n-dimensional Hom-Lie algebras over an algebraically closed field of characteristic zero is provided with a structure of algebraic subvariety of the affine plane of dimension n^2(n-1)/2}. For n=3, these two sets…

Let L(n-l+1/2,0) be the vertex operator algebra associated to an affine Lie algebra of type B_l^(1) at level n-l+1/2, for a positive integer n. We classify irreducible L(n-l+1/2,0)-modules and show that every L(n-l+1/2,0)-module is…

We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric,…

We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the…

We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine)…

We introduce some modified forms for the degenerate and non-degenerate affine Hecke algebras of type $A$. These are certain subalgebras living inside the inverse limit of cyclotomic Hecke algebras. We construct faithful representations and…

In this paper we determine the at least $4$-dimensional affine reductive homogeneous manifolds for an at most $9$-dimensional simple Lie group or an at most $6$-dimensional semi-simple Lie group. Those reductive spaces among them which…

In this paper we determine the partition into Kazhdan-Lusztig cells of the affine Weyl groups of type $\tB_{2}$ and $\tG_{2}$ for any choice of parameters. Using these partitions we show that the semicontinuity conjecture of Bonnaf\'e holds…

We consider discontinuous operations of a group $G$ on a contractible $n$-dimensional manifold $X$. Let $E$ be a finite dimensional representation of $G$ over a field $k$ of characteristics 0. Let $\mathcal{E}$ be the sheaf on the quotient…

Using brane quantization, we study the representation theory of the spherical double affine Hecke algebra of type $A_1$ in terms of the topological A-model on the moduli space of flat SL(2,C)-connections on a once-punctured torus. In…

Let $W$ be an irreducible Weyl group and $W_a$ its affine Weyl group. In this article we show that there exists a bijection between $W_a$ and the integral points of an affine variety, denoted $\widehat{X}_{W_a}$, which we call the Shi…

Let $G$ be a direct product of inner forms of general linear groups over non-archimedean locally compact fields of residue characteristic $p$ and let $K^1$ be the pro-$p$-radical of a maximal compact open subgroup of $G$. In this paper we…

To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…

We introduce the combinatorial model of $J$-folded alcove paths in an affine Weyl group and construct representations of affine Hecke algebras using this model. We study boundedness of these representations, and we state conjectures linking…

We define a noncommutative analogue of invariant de Rham cohomology. More precisely, for a triple $(A,\mathcal{H},M)$ consisting of a Hopf algebra $\mathcal{H}$, an $\mathcal{H}$-comodule algebra $A$, an $\mathcal{H}$-module $M$, and a…

This paper computes the irreducible characters of the alternating Hecke algebras, which are deformations of the group algebras of the alternating groups. More precisely, we compute the values of the irreducible characters of the semisimple…

We use the Hecke algebras of affine symmetric groups and their associated Schur algebras to construct a new algebra through a basis, and a set of generators and explicit multiplication formulas of basis elements by generators. We prove that…