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Permutation characters of finite groups of Lie type

Part of: Linear algebraic groups and related topics Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

David B. Surowski
David B. Surowski
Affiliation:
Kansas State UniversityManhattan, Kansas, USA
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Abstract

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Let g be a connected reductive linear algebraic group, and let G = gσ be the finite subgroup of fixed points, where σ is the generalized Frobenius endomorphism of g. Let x be a regular semisimple element of G and let w be a corresponding element of the Weyl group W. In this paper we give a formula for the number of right cosets of a parabolic subgroup of G left fixed by x, in terms of the corresponding action of w in W. In case G is untwisted, it turns out thta x fixes exactly as many cosets as does W in the corresponding permutation representation.

MSC classification

Secondary: 20C15: Ordinary representations and characters 20G05: Representation theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 3 , May 1979 , pp. 378 - 384
Copyright
Copyright © Australian Mathematical Society 1979

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