Generic decompositions of Deligne--Lusztig representations
Abstract
Let G0 be a reductive group over Fp with simply connected derived subgroup, (geometrically) connected center and Coxeter number h+1. We extend Jantzen's generic decomposition pattern from (2h-1)-generic to h-generic Deligne--Lusztig representations, which is optimal. We also prove several results on the ``obvious'' Jordan--H\"older factors of general Deligne--Lusztig representations. As an application we improve the weight elimination result of arXiv:1610.04819 [math.NT]
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