Mod $\ell$ Weil representations and Deligne--Lusztig inductions for unitary groups

Naoki Imai; Takahiro Tsushima

doi:10.1090/ert/685

Mod $\ell$ Weil representations and Deligne--Lusztig inductions for unitary groups

Representation Theory 2025-02-25 v2 Number Theory

Authors: Naoki Imai , Takahiro Tsushima

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Abstract

We study the mod $\ell$ Weil representation of a finite unitary group and related Deligne--Lusztig inductions. In particular, we study their decomposition as representations of a symplectic group, and give a construction of a mod $\ell$ Howe correspondence for $(\mathrm{Sp}_{2n},\mathrm{O}_2^-)$ including the case where $p=2$ .

Keywords

mod l weyl representation finite unitary group deligne-lusztig induction symplectic group howe correspondence

Cite

@article{arxiv.2002.05872,
  title  = {Mod $\ell$ Weil representations and Deligne--Lusztig inductions for unitary groups},
  author = {Naoki Imai and Takahiro Tsushima},
  journal= {arXiv preprint arXiv:2002.05872},
  year   = {2025}
}

Comments

26 pages

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