  In this paper, we deduce explicit multiplicity formulas of the Fourier-Jacobi
model for Deligne-Lusztig characters of finite symplectic groups, unitary
groups, and general linear groups. We then apply these results to deduce the
explicit depth zero local descent (\`a la Soudry and Tanay) for $p$-adic
unitary groups. The result is a concrete example in the context of non-tempered
Gan-Gross-Prasad program.
