The simplicial complex of Brauer pairs of a finite reductive group

IF 1 3区 数学 Q1 MATHEMATICS
Damiano Rossi
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引用次数: 0

Abstract

In this paper we study the simplicial complex induced by the poset of Brauer pairs ordered by inclusion for the family of finite reductive groups. In the defining characteristic case the homotopy type of this simplicial complex coincides with that of the Tits building thanks to a well-known result of Quillen. On the other hand, in the non-defining characteristic case, we show that the simplicial complex of Brauer pairs is homotopy equivalent to a simplicial complex determined by generalised Harish-Chandra theory. This extends earlier results of the author on the Brown complex and makes use of the theory of connected subpairs and twisted block induction developed by Cabanes and Enguehard.

Abstract Image

有限还原群的布劳尔对的简单复数
在本文中,我们研究了有限还原群族的布劳尔对的包含排序的正集所诱导的简单复数。在定义特征情况下,由于奎伦(Quillen)的一个著名结果,这个简单复数的同调类型与蒂茨楼的同调类型重合。另一方面,在非定义特征情况下,我们证明布劳尔对的单纯复数与广义哈里什-钱德拉理论确定的单纯复数同调等价。这扩展了作者早先关于布朗复数的结果,并利用了卡巴内斯和恩格哈德发展的连通子对理论和扭块归纳法。
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来源期刊
CiteScore
1.60
自引率
0.00%
发文量
236
审稿时长
3-6 weeks
期刊介绍: "Mathematische Zeitschrift" is devoted to pure and applied mathematics. Reviews, problems etc. will not be published.
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