Agoh, Takashi Shoji, Toshiaki
Published in
Monatshefte für Mathematik

Letp be an odd prime and\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{F}_p $$ \end{document} the finite field withp elements. In the present paper we shall i...

Il’yuta, G. G.
Published in
Mathematical Notes

We prove relations in the braid group that generalize the relations of the formaba=bab. These relations are obtained by means of the generalization to the higher Bruhat orders of the well-known relation between the decompositions of the element of maximal length in the Weyl groupAn−1 and some specific linear orders on the system of positive roots o...

Gerstenhaber, Murray Giaquinto, Anthony Schaps, Mary E.
Published in
Letters in Mathematical Physics

The Donald–Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and Weyl groups of types Bn and Dn (whose rational group algebras are computed), leaving but six finite reflection groups with solutions unknown. We determine the struct...

Reeder, Mark
Published in
Compositio Mathematica

The space of elliptic virtual representations of a p-adic group is endowed with a natural inner product EP( , ), defined analytically by Kazhdan and homologically by Schneider–Stuhler. Arthur has computed EP in terms of analytic R-groups. For Iwahori spherical representations, we show that EP can also be expressed in terms of a corresponding inner ...

Bonnafé, Cédric

We construct a new isomorphism between the endomorphism algebra of an induced cuspidal character sheaf and the group algebra of the relative Weyl group involved. We show it differs from Lusztig one by a linear character, and we relate this linear character to some stabilizers. Some consequences on characteristic functions of character sheaves are o...

Hezard, David

Soit G un groupe algébrique réductif connexe de centre connexe défini sur un corps fini de caractéristique p>0. On munit cette structure d'un endomorphisme de Frobenius F et l'on note G^F l'ensemble des points de G fixes pour l'action de F : G^F est un groupe fini. On suppose que la caractéristique p est bonne pour G.

On définit alors une applicatio...

Bonnafé, Cédric

The aim of this second part is to compute explicitly the Lusztig restriction of the characteristic function of a regular unipotent class of a finite reductive group, improving slightly a theorem of Digne, Lehrer and Michel. We follow their proof but introduce new information, namely the computation of morphisms $\varphi_{L,v}^G$ defined in the firs...

Juteau, Daniel

In 1976, Springer defined a correspondence making a link between the irreducible ordinary (characteristic zero) representations of a Weyl group and the geometry of the associated nilpotent variety. In this thesis, we define a modular Springer correspondence (in positive characteristic), and we show that the decomposition numbers of a Weyl group (fo...

Azam, Saeid Shahsanaei, Valiollah
Published in
Journal of Algebraic Combinatorics

It is known that elliptic Weyl groups, extended affine Weyl groups of nullity 2, have a finite presentation called the generalized Coexter presentation. Similar to the finite and affine case this presentation is obtained by assigning a Dynkin diagram to the root system. Then there is a prescription to read the generators and relations from the diag...

Burdges, Jeffrey Deloro, Adrien
Published in
Israel Journal of Mathematics

We examine Weyl groups of minimal connected simple groups of finite Morley rank of degenerate type. We show that they are cyclic, and lift isomorphically to subgroups of the ambient group.