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The simplicial complex of Brauer pairs of a finite reductive group.

The simplicial complex of Brauer pairs of a finite reductive group.

Authors :
Rossi, Damiano
Source :
Mathematische Zeitschrift; Oct2024, Vol. 308 Issue 2, p1-11, 11p
Publication Year :
2024

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 FROM AUTHOR]

Details

Language :
English
ISSN :
00255874
Volume :
308
Issue :
2
Database :
Complementary Index
Journal :
Mathematische Zeitschrift
Publication Type :
Academic Journal
Accession number :
179315685
Full Text :
https://doi.org/10.1007/s00209-024-03579-5