Extending the Steinberg representation
type: Item
instance of: scholarly article
title: Extending the Steinberg representation
zbMATH Open document ID: 0794.20022
DOI: 10.1016/S0021-8693(05)80060-2
author: Peter Schmid
published in: Journal of Algebra
publication date: 1992-09-27T00:00:00Z
review text: Let \(G\) be a finite group with a split \(BN\)-pair of rank \(n\geq 1\) and characteristic \(p\), and let \(St_ G\) be its Steinberg character. The author [Linear Algebra Appl. 71, 289-293 (1985; Zbl 0575.20005)] has shown that the Steinberg representation can be extended to any group \(E\) containing \(G\) as a normal subgroup. In the present paper the author gives a more natural approach which is based on a nice description of the Steinberg module. The key proposition provides a \(\mathbb{Q} G\)-homomorphism whose kernel affords the Steinberg character.
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20E42
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 63905
zbMATH Keywords: finite group
zbMATH Keywords: split BN-pair
zbMATH Keywords: Steinberg character
zbMATH Keywords: Steinberg representation
zbMATH Keywords: Steinberg module
MaRDI profile type: Publication
cites work: Q5658847
cites work: Q4724810
cites work: Rational matrix groups of a special type
description: scientific article; zbMATH DE number 63905