Coxeter orbits and Brauer trees

Abstract

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, Lübeck and Malle) and the derived equivalence predicted by the geometric version of Broué's conjecture.

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

References in corpus (4)

• Derived equivalences for symmetric groups and sl\_2-categorification
• Parabolic Deligne-Lusztig varieties
• Perverse Equivalences and Broué's Conjecture II: The Cyclic Case
• On the Cohomology of Deligne-Lusztig Varieties

Cited by in corpus (5)

• Perverse Equivalences and Broué's Conjecture II: The Cyclic Case
• On the Cohomology of Deligne-Lusztig Varieties
• Jordan decomposition for weights and the blockwise Alperin weight conjecture
• The Brauer trees of unipotent blocks
• A geometric interpretation of the nilpotent part of local Langlands correspondence modulo l