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arXiv · 2208.02308

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

Dongwen Liu·Jia-Jun Ma·Fang Shi
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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.

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Dongwen Liu, Jia-Jun Ma, Fang Shi. 2022-08-03. Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups. https://arxiv.org/abs/2208.02308

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