由抛物群导出的置换模的各分量的顶点

Pub Date : 2018-10-01 DOI:10.18910/70821

Lars Pforte

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引用次数: 0

摘要

我们考虑置换模kP↑其中p是一般线性群GLn（pf）中的抛物群，k是素数特征p的代数闭域。Tinberg在[9]中计算了这些模的分量的顶点，他研究了特征p中具有分裂BN对的所有群的这些模。在本文中，我们证明了适用性的思想足够强，可以找到所有p群都是kP的某个分量的顶点↑GLn（pf）。此外，利用Burry和Carlson的结果，我们证明了所有组件都有一个不同的顶点。

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THE VERTICES OF THE COMPONENTS OF THE PERMUTATION MODULE INDUCED FROM PARABOLIC GROUPS

We consider the permutation module kP↑GLn(p f ), where P is a parabolic group in the general linear group GLn(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 kP↑GLn(p f ). Furthermore using a result of Burry and Carlson we show that all components have a different vertex.

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