On some characters of \(GL_ n(2)\)
type: Item
instance of: scholarly article
title: On some characters of \(GL_ n(2)\)
zbMATH Open document ID: 0553.20022
DOI: 10.1016/0022-4049(85)90043-X
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let V be the vector space of dimension at least 3 over the field of two elements. Let G be the general linear group acting on V. Let \(\theta\) be the nonidentity constituent of the permutation character from G acting on the nonzero elements of V. Let \(\Delta\) be the set of all ordered pairs where the components are a hyperplane of V and a vector not in that hyperplane. Let \(\xi\) be the permutation character of G on \(\Delta\). The author finds the irreducible constituents of \(\xi\). In fact, \(\xi =1+2\theta +\phi +\psi\) where \(\phi\) is a character obtained by Steinberg and \(\psi\) is apparently new.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 3880936
zbMATH Keywords: general linear group
zbMATH Keywords: permutation character
zbMATH Keywords: irreducible constituents
author: M. R. Darafsheh
MaRDI profile type: Publication
cites work: Transitivity of finite permutation groups on unordered sets
cites work: A Geometric Approach to the Representations of the Full Linear Group Over a Galois Field
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description: scientific article; zbMATH DE number 3880936