Generic decompositions of Deligne--Lusztig representations

Daniel Le; Bao V. Le Hung; Brandon Levin; Stefano Morra

paper

Generic decompositions of Deligne--Lusztig representations

arXiv:2405.18002

Abstract

Let $G_{0}$ be a reductive group over $F_{p}$ with simply connected derived subgroup, (geometrically) connected center and Coxeter number $h + 1$ . We extend Jantzen's generic decomposition pattern from $(2 h - 1)$ -generic to $h$ -generic Deligne--Lusztig representations, which is optimal. We also prove several results on the ``obvious'' Jordan--Hölder factors of general Deligne--Lusztig representations. As an application we improve the weight elimination result of arXiv:1610.04819 [math.NT]

Revised version after the referee's report