Related papers: Computing groups of Hecke characters

Hecke algebras are beautiful q-extensions of Coxeter groups. In this paper, we prove several results on their characters, with an emphasis on characters induced from trivial and sign representations of parabolic subalgebras. While most of…

We introduce the generic central character of an irreducible discrete series representation of an affine Hecke algebra. Using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine…

The families of characters, defined by Lusztig for Weyl groups, play an important role in the representation theory of finite reductive groups. The definition of Rouquier for the families of characters in terms of blocks of the Hecke…

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…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

We present an algorithm to compute the Hecke operators on the equivariant cohomology of an arithmetic subgroup $\Gamma$ of the general linear group $\mathrm{GL}_n$. This includes $\mathrm{GL}_n$ over a number field or a finite-dimensional…

It is known that characters of irreducible representations of finite Lie algebras can be obtained using theWeyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras…

We associate infinitesimal characters to (twisted) families of $L$-parameters and $C$-parameters of $p$-adic reductive groups. We use the construction to study the action of the centre of the universal enveloping algebra on the locally…

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…

We give a new and independent parameterization of the set of discrete series characters of an affine Hecke algebra $\mathcal{H}_{\mathbf{v}}$, in terms of a canonically defined basis $\mathcal{B}_{gm}$ of a certain lattice of virtual…

This paper describes an approach to computer aided calculations in the cohomology of arithmetic groups. It complements existing literature on the topic by emphasizing homotopies and perturbation techniques, rather than cellular subdivision,…

We use vertex operators to compute irreducible characters of the Iwahori-Hecke algebra of type $A$. Two general formulas are given for the irreducible characters in terms of those of the symmetric groups or the Iwahori-Hecke algebras in…

We establish a lower bound for the representation dimension of all the classical Hecke algebras of types A, B and D. For all the type A algebras, and most of the algebras of types B and D, we also establish upper bounds. Moreover, we…

I calculate characters of certain representations of loop groups based on non simply connected Lie groups. This gives a generalization of the Kac-Weyl character formula.

We discuss several arithmetic aspects of Bianchi groups, especially from a computational point of view. In particular, we consider computing the homology of Bianchi groups together with the Hecke action, connections with automorphic forms,…

The "Rouquier blocks" of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the "families of characters", defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article,…

In this paper we establish the explicit exponential map for the Galois representation from a Hecke character at an ordinary prime. Such explicit maps are important in verifying the Bloch-Kato conjecture for Hecke characters.

Let $\pi, \pi'$ be irreducible tempered representations of an affine Hecke algebra H with positive parameters. We compute the higher extension groups $Ext_H^n (\pi,\pi')$ explicitly in terms of the representations of analytic R-groups…

We prove a reciprocity law for one-dimensional compatible systems of mod p representations of absolute Galois groups of number fields. We prove that these arise from Hecke characters, and in particular recover by purely algebraic means the…