Linear characters of finite linear groups
type: Item
instance of: scholarly article
title: Linear characters of finite linear groups
zbMATH Open document ID: 0932.20048
author: Nicholas F. J. Inglis
published in: Journal of Algebra
publication date: 2000-01-13T00:00:00Z
review text: Let \(V\) be a vector space of dimension \(n\) over the field \(\mathbb{F}_q\) of order \(q\), let \(G\) be a subgroup of \(\text{GL}(V)\), and let \(Y\) be a \(G\)-invariant subset of the set \({\mathcal P}(V)\) of \(1\)-spaces of \(V\). The author defines an \(\mathbb{F}_q^*\)-valued linear character \(\delta_Y\) related to the permutation action of \(G\) on \(Y\) and to the associated action of \(G\) on vectors. He shows that special cases of this character include both the determinant when \(G\) is the general linear group and the spinor norm when \(q\) is odd and \(G\) is an orthogonal group. This formulation is particularly useful when one is considering \(G\) as the Galois group of a polynomial.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 1295428
zbMATH Keywords: general linear groups
zbMATH Keywords: spinor norms
zbMATH Keywords: linear characters
zbMATH Keywords: determinants
zbMATH Keywords: actions
MaRDI profile type: Publication
full work available at URL: jabr.1997.7348
OpenAlex ID: W2068770847
DOI: 10.1006/JABR.1997.7348
description: scientific article; zbMATH DE number 1295428