Descents of unipotent representations of finite unitary groups

2019/04/17 by Dongwen Liu, Zhicheng Wang, Liu, Dongwen +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1904.08188

openalex publication_date 2019/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Restrictions of representations of classical groups: examples

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