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October 2018 The vertices of the components of the permutation module induced from parabolic groups
Lars Pforte
Osaka J. Math. 55(4): 769-775 (October 2018).

Abstract

We consider the permutation module $k_P{\uparrow^{{\rm GL}_n(p^f)}}$, where $P$ is a parabolic group in the general linear group ${\rm GL}_n(p^f)$ and $k$ is an algebraically closed field of prime characteristic $p$. The vertices of the components of these modules have been calculated in [9] by Tinberg, who studied these modules for all groups with split BN-pairs in characteristic $p$. In this paper we show that the idea of suitability is strong enough to find all $p$-groups that are vertex of some component of $k_P{\uparrow^{{\rm GL}_n(p^f)}}$. Furthermore using a result of Burry and Carlson we show that all components have a different vertex.

Citation

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Lars Pforte. "The vertices of the components of the permutation module induced from parabolic groups." Osaka J. Math. 55 (4) 769 - 775, October 2018.

Information

Published: October 2018
First available in Project Euclid: 10 October 2018

zbMATH: 06985312
MathSciNet: MR3862785

Subjects:
Primary: 20G40

Rights: Copyright © 2018 Osaka University and Osaka City University, Departments of Mathematics

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Vol.55 • No. 4 • October 2018
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