Discrete series characters for \(\text{GL}(n,q)\)
type: Item
instance of: scholarly article
title: Discrete series characters for \(\text{GL}(n,q)\)
zbMATH Open document ID: 0931.20037
DOI: 10.1023/A:1009975523963
author: James A. Green
published in: Algebras and Representation Theory
publication date: 1999-09-28T00:00:00Z
review text: The `discrete series' characters of the finite general linear group \(\text{GL}(n,q)\) are those ordinary, irreducible characters which are not constituents of the permutation character induced from the radical of any proper parabolic subgroup of \(\text{GL}(n,q)\). They cannot be obtained by `Harish-Chandra induction' from characters of \(\text{GL}(n',q)\) for \(n'<n\), nor expressed as linear combinations of characters induced from proper parabolic subgroups of \(\text{GL}(n,q)\). Various methods are known for calculating these discrete series characters but the paper under review presents them in a particularly simple fashion, as \(\mathbb{Z}\)-linear combinations of characters induced from linear characters on certain subgroups of \(\text{GL}(n,q)\).
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 1310750
zbMATH Keywords: discrete series characters
zbMATH Keywords: finite general linear groups
zbMATH Keywords: modular representations
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: induced characters
zbMATH Keywords: linear combinations of characters
reviewed by: Martin D. Crossley
MaRDI profile type: Publication
full work available at URL: a:1009975523963
OpenAlex ID: W1541445605
description: scientific article; zbMATH DE number 1310750