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

We study the mod $\mathrm{\ell }$ 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 $\mathrm{\ell }$ Howe correspondence for $({\mathrm{S}\mathrm{p}}_{2n},{\mathrm{O}}_2^{-})$ including the case where $p=2$.