On the inducing of unipotent classes for semisimple algebraic groups. I: Case of exceptional type
type: Item
instance of: scholarly article
title: On the inducing of unipotent classes for semisimple algebraic groups. I: Case of exceptional type
zbMATH Open document ID: 0539.20021
author: Takeshi Hirai
published in: Proceedings of the Japan Academy. Series A
publication date: 1982-01-01T00:00:00Z
review text: Let \(G\) be a connected semisimple algebraic group over an algebraically closed field \(K\). Let \(P\) be a parabolic subgroup of \(G\), \(L\) a Levi subgroup and \(U_ P\) the unipotent radical of \(P\). For a conjugate class \(C\) of unipotent elements in \(L\), the induced class \(C'=\mathrm{Ind}^ G_{L,P}C\) is defined as the unique class in \(G\) which intersects \(CU_ P\) densely [cf. \textit{G. Lusztig} and \textit{N. Spaltenstein}, J. Lond. Math. Soc., II. Ser. 19, 41--52 (1979; Zbl 0407.20035)]. Assuming that the characteristic of \(K\) is zero, the author studies how one can determine \(C'\) from \(C\) explicitly, when \(G\) is of exceptional type.
reviewed by: Şerban A. Basarab
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14L35
zbMATH DE Number: 3857368
zbMATH Keywords: Dynkin diagrams
zbMATH Keywords: Richardson classes
zbMATH Keywords: connected semisimple algebraic group
zbMATH Keywords: parabolic subgroup
zbMATH Keywords: Levi subgroup
zbMATH Keywords: unipotent radical
MaRDI profile type: Publication
full work available at URL: pjaa.58.37
OpenAlex ID: W4241309425
cites work: Zum Induzieren unipotenter Klassen
cites work: Polarizations in the classical groups
cites work: On Richardson classes of unipotent elements in semisimple algebraic groups
cites work: Induced Unipotent Classes
cites work: The conjugate classes of unipotent elements of the Chevalley groups \(E_ 7\) and \(E_ 8\).
DOI: 10.3792/PJAA.58.37
description: scientific article; zbMATH DE number 3857368