Generic decompositions of Deligne--Lusztig representations

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

Generic decompositions of Deligne--Lusztig representations

Representation Theory 2025-01-15 v2 Number Theory

Authors: Daniel Le , Bao V. Le Hung , Brandon Levin , Stefano Morra

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]

Keywords

Deligne–Lusztig representations generic decomposition reductive group Coxeter number Jordan–Hölder factors weight elimination

Cite

@article{arxiv.2405.18002,
  title  = {Generic decompositions of Deligne--Lusztig representations},
  author = {Daniel Le and Bao V. Le Hung and Brandon Levin and Stefano Morra},
  journal= {arXiv preprint arXiv:2405.18002},
  year   = {2025}
}

Comments

Revised version after the referee's report

Generic decompositions of Deligne--Lusztig representations

Abstract

Keywords

Cite

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