Related papers: An involution based left ideal in the Hecke algebr…
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…
We study Kazhdan-Lusztig cells and the corresponding representations of right-angled Coxeter groups and Hecke algebras associated to them. In case of the infinite groups generated by reflections in the hyperbolic plane about the sides of…
We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are…
Let $A_1$ be the (first) Weyl algebra, and let $G$ be its automorphism group. We study the natural action of $G$ on the space of isomorphism classes of right ideals of $A_1$ (equivalently, of finitely generated rank 1 torsion-free right…
Let F be a nonarchimedean local field of odd residual characteristic p. We classify finite-dimensional simple right modules for the pro-p-Iwahori-Hecke algebra $\mathcal{H}_C(G,I(1))$, where G is the unramified unitary group U(2,1)(E/F) in…
Soergel bimodule category B is a categorification of the Hecke algebra of a Coxeter system (W,S). We find a presentation of B (as a tensor category) by generators and relations when W is a right-angled Coxeter group.
These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…
We consider a Hecke algebra naturally associated with the affine group with totally positive multiplicative part over an algebraic number field K and we show that the C*-algebra of the Bost-Connes system for K can be obtained from our Hecke…
The Kac-Moody affine Hecke algebra $\mathcal{H}$ was first constructed as the Iwahori-Hecke algebra of a $p$-adic Kac-Moody group by work of Braverman, Kazhdan, and Patnaik, and by work of Bardy-Panse, Gaussent, and Rousseau. Since…
We attach to every Coxeter system (W,S) an extension C_W of the corresponding Iwahori-Hecke algebra. We construct a 1-parameter family of (generically surjective) morphisms from the group algebra of the corresponding Artin group onto C_W.…
In this paper, we let $\Hecke$ be the Hecke algebra associated with a finite Coxeter group $W$ and with one-parameter, over the ring of scalars $\Alg=\mathbb{Z}(q, q^{-1})$. With an elementary method, we introduce a cellular basis of…
For $W$ a Coxeter group, let $\mathcal{W} = \{ w \in W \;| \; w = xy \; \mbox{where} \; x, y \in W \; \mbox{and} \; x^2 = 1 = y^2 \}$. If $W$ is finite, then it is well known that $W = \mathcal{W}$. Suppose that $w \in \mathcal{W}$. Then…
We study the Hecke algebra $\H(\bq)$ over an arbitrary field $\FF$ of a Coxeter system $(W,S)$ with independent parameters $\bq=(q_s\in\FF:s\in S)$ for all generators. This algebra is always linearly spanned by elements indexed by the…
Let $(W,S)$ be a Coxeter system. A $W$-graph encodes a representation of the Hecke algebra $\mathcal{H}$ of $W$. We construct universal representations of multi-parameter Hecke algebras on certain quotients of path algebras, and study their…
The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum…
The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a…
In this paper we outline the Hecke theory for Hermitian modular forms in the sense of Hel Braun for arbitrary class number of the attached imaginary-quadratic number field. The Hecke algebra turns out to be commutative. Its inert part has a…
Lie-theoretic structures of type $E_8$ (e.g., Lie groups and algebras, Hecke algebras and Kazhdan-Lusztig cells, ...) are considered to serve as a `gold standard' when it comes to judging the effectiveness of a general algorithm for solving…
We introduce and study some affine Hecke algebras of type ADE, generalising the affine Hecke algebras of GL. We construct irreducible calibrated representations and describe the calibrated spectrum. This is done in terms of new families of…
Involution words are variations of reduced words for twisted involutions in Coxeter groups. They arise naturally in the study of the Bruhat order, of certain Iwahori-Hecke algebra modules, and of orbit closures in flag varieties.…