Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups

Abstract: 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.