  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
$p=2$.
