Related papers: Harish-Chandra Induction and Jordan Decomposition …

In this paper, we begin with the classification of Harish-Chandra imprimitive representations in non-defining characteristic. We recall the connection of this problem to certain generalizations of Iwahori-Hecke algebras and show that…

The aim of this article is to give a complete proof of results of Harish-Chandra linking the irreducibility of parabolic induction of a supercuspidal representation of a p-adic group to the analytic behavior of the mu-function of…

We use the progenerator constructed in our previous paper to give a necessary condition for a simple module of a finite reductive group to be cuspidal, or more generally to obtain information on which Harish-Chandra series it can lie in. As…

We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element in the dual group is connected, then the map is Galois-equivariant. Further, in this…

For any complex reductive Lie algebra g and any locally finite g-module V, we extend to the tensor product of U(g) with V the Harish-Chandra description of g-invariants in the universal enveloping algebra U(g).

In this article we consider the centre of the reduced enveloping algebra of the Lie algebra of a reductive algebraic group in very good characteristic p > 2. The Harish-Chandra centre maps to the centre of each reduced enveloping algebra…

Let G be the group of rational points of a connected reductive group over a finite field. Based on work of Lusztig and Yun, we make the Jordan decomposition for irreducible G-representations canonical. It comes in the form of an equivalence…

Given a supercuspidal representation $\sigma$ of a parabolic subgroup $P$ of reductive group $G$, we discover a universal hierarchical structure of reducibility of the parabolic induction $Ind^G_P(\sigma)$, i.e. always irreducible from some…

Let G be a reductive connected p-adic group. With help of the Fourier inversion formula used in [Une formule de Plancherel pour l'algebre de Hecke d'un groupe reductif p-adique - V. Heiermann, Comm. Math. Helv. 76, 388-415, 2001] we give a…

We construct a pinned canonical Jordan decomposition of characters for finite reductive groups in cases where the relevant dual centralizers may be disconnected. For a connected reductive group \(G\) over a finite field, with a fixed…

Let $\bf{G}$ be a connected reductive group with connected center defined over $\mathbb{F}_q$, with Frobenius morphism $F$. We parameterize all of the real-valued irreducible complex characters of ${\bf G}^F$ using the Jordan decomposition…

For any reductive Lie algebra $\mathfrak{g}$ and commutative, associative, unital algebra $S$, we give a complete classification of the simple weight modules of $\mathfrak{g}\otimes S $ with finite weight multiplicities. In particular, any…

The irreducible characters of a finite reductive group are partitioned into Harish-Chandra series that are labelled by cuspidal pairs. In this note, we describe how one can algorithmically calculate those cuspidal pairs using results of…

We give a geometric account of Harish-Chandra's principle that a tempered irreducible representation of a real reductive group is either square-integrable modulo center, or embeddable in a representation that is parabolically induced from…

Let $\mathbf{G}$ be a connected reductive group with connected center defined over $\mathbb{F}_q$, with Frobenius morphism F. Given an irreducible complex character $\chi$ of $\mathbf{G}^F$ with its Jordan decomposition, and a Galois…

We examine from an algebraic point of view some families of unitary group representations that arise in mathematical physics and are associated to contraction families of Lie groups. The contraction families of groups relate different real…

In this paper we show that any linear vector field $\mathcal{X}$ on a connected Lie group $G$ admits a Jordan decomposition and the recurrent set of the associated ow of automorphisms is given as the intersection of the fixed points of the…

This article is a record of the lecture at the centennial conference for Harish-Chandra. The admissibility theorem of Harish-Chandra concerns the restrictions of irreducible representations to maximal compact subgroups. In this article, we…

In this article we prove that the elliptic, hyperbolic and nilpotent (or unipotent) additive (or multiplicative) Jordan components of an endomorphism $X$ (or an isomorphism $g$) of a finite dimensional vector space are given by polynomials…

As shown by Bonnaf\'e, a step in proving a Jordan decomposition of characters of finite special linear groups is the parametrization of unipotent characters of centralizers of semi-simple elements in projective linear groups. We show the…