Die Quasiaffinität der Deligne-Lusztig-Varietäten. (The quasi- affinity of the Deligne-Lusztig varieties)
type: Item
instance of: scholarly article
title: Die Quasiaffinität der Deligne-Lusztig-Varietäten. (The quasi- affinity of the Deligne-Lusztig varieties)
zbMATH Open document ID: 0615.20021
DOI: 10.1016/0021-8693(86)90135-3
author: Burkhard Haastert
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let G be a connected reductive algebraic group over the finite field with q elements. The socalled Deligne-Lusztig varieties in G/B, B a Borel subgroup, are known to be affine for q large by the work of \textit{P. Deligne} and \textit{G. Lusztig} [Ann. Math., II. Ser. 103, 103-161 (1976; Zbl 0336.20029)]. In this paper, the author proves that these varieties are always quasi-affine. This allows him then to generalize several of Deligne's and Lusztig's results including their vanishing theorem and statements about the eigenvalues of the Frobenius endomorphism of the non-vanishing cohomology group.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 3995966
zbMATH Keywords: connected reductive algebraic group
zbMATH Keywords: Deligne-Lusztig varieties
zbMATH Keywords: Borel subgroup
zbMATH Keywords: quasi-affine
zbMATH Keywords: vanishing theorem
zbMATH Keywords: eigenvalues of the Frobenius endomorphism
reviewed by: Henning Haahr Andersen
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90135-3
OpenAlex ID: W2050082310
cites work: Désingularisation des variétés de Schubert généralisées
cites work: Representations of reductive groups over finite fields
cites work: Q3904770
cites work: Fonctions $L$ des variétés de Deligne-Lusztig et descente de Shintani
cites work: Algebraic groups and Hopf algebras
cites work: Irreducible representations of finite classical groups
cites work: Q4217748
cites work: Q3871006
cites work: Q5587150
description: scientific article; zbMATH DE number 3995966