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

Naoki Imai, Takahiro Tsushima

Published 2020-02-14Version 1

We study a decomposition of the mod $\ell$ Weil representation of a finite unitary group via Deligne--Lusztig inductions. We study also its decomposition as representations of a symplectic group, and give a construction of mod $\ell$ Howe correspondence for $(\mathit{Sp}_{2n},O_2^-)$ including the case where $p=2$.