The simplicial complex of Brauer pairs of a finite reductive group Article Swipe

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Mathematics Brauer group Simplicial complex Finite group Pure mathematics Group (periodic table) Combinatorics Reductive group Brauer's theorem on induced characters Abstract simplicial complex Algebra over a field Group theory Organic chemistry Chemistry

Damiano Rossi ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.1007/s00209-024-03579-5 · OA: W4401801710

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.