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

TL;DR

This paper derives explicit formulas for Fourier-Jacobi models of Deligne-Lusztig characters in finite groups and applies these to establish depth zero local descent for p-adic unitary groups, contributing to the Gan-Gross-Prasad program.

Contribution

It provides the first explicit multiplicity formulas for Fourier-Jacobi models of Deligne-Lusztig characters and applies them to depth zero local descent in p-adic unitary groups.

Findings

Explicit multiplicity formulas for Fourier-Jacobi models

Application to depth zero local descent for p-adic unitary groups

Concrete example in non-tempered Gan-Gross-Prasad context

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.