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

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 $p=2$.

26 pages