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arXiv · 2405.18002

Generic decompositions of Deligne--Lusztig representations

Daniel Le·Bao V. Le Hung·Brandon Levin·Stefano Morra
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Abstract

Let $G_0$ be a reductive group over $\mathbb{F}_p$ 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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Daniel Le, Bao V. Le Hung, Brandon Levin, Stefano Morra. 2024-05-28. Generic decompositions of Deligne--Lusztig representations. https://arxiv.org/abs/2405.18002

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