Related papers: Rationality of extended unipotent characters

We show that Ax-Katz divisibility on the number of rational points of a variety defined over a finite field by equations of low degrees comes from divisibility of the eigenvalues of the Frobenius action of the $\ell$-adic cohomology with…

Orthogonality relations for Foulkes characters of full monomial groups are presented, along with three solutions to the problem of decomposing products of these characters, and new applications, including a product reformulation of a Markov…

Let G be a reductive algebraic group over the algebraic closure of a finite field F_q of good characteristic. In this paper, we demonstrate a remarkable compatibility between the Springer correspondence for G and the parametrization of…

We derive a Murnaghan--Nakayama type formula for the values of unipotent characters of finite classical groups on regular semisimple elements. This relies on Asai's explicit decomposition of Lusztig restriction. We use our formula to show…

Suppose that a finite group $G$ admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup $C_G(H)$ of the complement is nilpotent of class $c$. It is proved that…

In this paper we study higher level Deligne--Lusztig representations of reductive groups over discrete valuation rings, with finite residue field $\mathbb{F}_q$. In previous work we proved that, at even levels, these geometrically…

We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.

Even with the introduction of supercharacter theories, the representation theory of many unipotent groups remains mysterious. This paper constructs a family of supercharacter theories for normal pattern groups in a way that exhibit many of…

We calculate the exact amenability constant of the centre of $\ell^1(G)$ when $G$ is one of the following classes of finite group: dihedral; extraspecial; or Frobenius with abelian complement and kernel. This is done using a formula which…

Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that the fixed-point subgroup of $F$ is trivial: $C_G(F)=1$. In this situation various properties of $G$ are shown to be…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

In this paper we obtain a decomposition formula of the uniform projection of the Weil character of a finite reductive dual pair consisting of a symplectic group and an even orthogonal group. This is the first and major step to give an…

We generalize the positive solution of the Frobenius conjecture and refinements thereof by studying the structure of groups that admit a fix-point-free automorphism satisfying an identity. We show, in particular, that for every polynomial…

Let $G$ be a connected reductive algebraic group defined over the finite field $\FF_q$, where $q$ is a power of a good prime for $G$. We write $F$ for the Frobenius morphism of $G$ corresponding to the $\FF_q$-structure, so that $G^F$ is a…

This paper is concerned with the representation theory of finite groups. According to Robinson, the truth of certain variants of Alperin's weight conjecture on the $p$-blocks of a finite group would imply some arithmetical conditions on the…

The algorithm of computing generalized Green functions of a finite reductive group contains some unkonwn scalars occuring from the F_q structure of irreducible local systems on unipotent classes on G. In this paper, we determine such…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

This note is concerned with the unipotent characters of the Ree groups of type G_2. We determine the roots of unity associated by Lusztig and Digne-Michel to unipotent characters of ^2G_2(3^{2n+1}) and we prove that the Fourier matrix of…

Let $G$ be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to $3$. We construct a canonical correspondence between irreducible characters of degree coprime to $3$ of $G$ and those…

Let G(F_q) be the group of rational points of a simple algebraic group defined and split over a finite field F_q. In this paper we define a new basis for the Grothendieck group of unipotent representations of G(F_q).