Descents of unipotent representations of finite unitary groups

TL;DR

This paper explicitly determines the descents of unipotent representations of finite unitary groups, covering Bessel and Fourier-Jacobi cases, and explores their relation via theta correspondence.

Contribution

It provides the first explicit descriptions of unipotent representation descents for finite unitary groups, advancing understanding of their structure and relations.

Findings

Explicit descents of unipotent representations are unipotent.

Results include Bessel and Fourier-Jacobi cases.

Connections via theta correspondence are established.

Abstract

Inspired by the Gan-Gross-Prasad conjecture and the descent problem for classical groups, in this paper we study the descents of unipotent representations of unitary groups over finite fields. We give the first descents of unipotent representations explicitly, which are unipotent as well. Our results include both the Bessel case and Fourier-Jacobi case, which are related via theta correspondence.