Coxeter orbits and Brauer trees

Details Coxeter orbits and Brauer trees Coxeter orbits and Brauer trees

2010-11-24

arxiv.org/abs/1011.5476v2

Advances in Mathematics 229, 6 (2012) 3398--3435

Mathematics

Representation Theory

v2: minor corrections (including the Brauer tree of 2G2)

Scientific paper

10.1016/j.aim.2012.02.011

We study the cohomology with modular coefficients of Deligne-Lusztig varieties associated to Coxeter elements. Under some torsion-free assumption on the cohomology we derive several results on the principal l-block of a finite reductive group G(F_q) when the order of q modulo l is assumed to be the Coxeter number. These results include the determination of the planar embedded Brauer tree of the block (as conjectured by Hiss, L\"ubeck and Malle) and the derived equivalence predicted by the geometric version of Brou\'e's conjecture.

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