Related papers: A remark on some bases in the Hecke algebra
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
In this paper we prove a conjecture on the dimension of linear systems, with base points of multiplicity 2 and 3, on an Hirzebruck surface.
We introduce and study expansions of real numbers with respect to two integer bases.
We show that, in a highest weight category with duality, the endomorphism algebra of a tilting object is naturally a cellular algebra. Our proof generalizes a recent construction of Andersen, Stroppel, and Tubbenhauer. This result raises…
We review the construction of generalized affine Hecke algebras attached to Bernstein series of both smooth irreducible and enhanced $L$-parameters of $p$-adic reductive groups and apply it to the study of the Howe correspondence.
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
We study the representation theory of graded Hecke algebras, starting from scratch and focusing on representations that are obtained with induction from a discrete series representation of a parabolic subalgebra. We determine all…
Given an affine hyperplane arrangement with some additional structure, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul…
A discrete duality is a relationship between classes of algebras and classes of relational systems (frames) resulting in two representation theorems building on the early work of J\'onsson and Tarski, Kripke, and van Benthem. In this…
We study star operations for Iwahori-Hecke algebras and invariant hermitian forms for finite dimensional modules over (graded) affine Hecke algebras with a view towards a unitarity algorithm.
This paper constructs a representation of a Hecke algebra on a vector space spanned by the involutions in a Coxeter group.
We show that the transition matrix from the standard basis to the web basis for a Specht module of the Hecke algebra is unitriangular and satisfies a strong positivity property whenever the Specht module is labeled by a partition with at…
This lecture reviews the classification of simple modules of double affine Hecke algebras via the K-theory of Steinberg varieties of affine type
Howe's duality is considered from a unifying point of view based on Lie superalgebras. New examples are offered. In particular, we construct several simplest spinor-oscillator representations and compute their highest weights for the…
Algebraic deformations of modules over a ring are considered. The resulting theory closely resembles Gerstenhaber's deformation theory of associative algebras.
We give two generalizations of the Alvis-Curtis duality for Hecke algebras: an unequal parameter version for the affine Hecke algebras, based on S.-I. Kato's work, and a relative version for finite Hecke algebras, based on Howlett-Lehrer's…
In \cite{AC12}, among other things, we observed that the structure constants of the Hecke algebra of the Gel'fand pair $(S_{2n},B_n)$ are polynomials in $n$. It is brought to attention by Omar Tout that there is a missing argument in its…
We notice that for any positive integer $k$, the set of $(1,2)$-specialized characters of level $k$ standard $A_{1}^{(1)}$-modules is the same as the set of rescaled graded dimensions of the subspaces of level $2k+1$ standard…
In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.
After reviewing classical Schur-Weyl duality, we present some other contexts which enjoy similar features, relating to Brauer algebras and classical groups.