On the Jacquet functor of Symplectic groups

2024/05/10 by Prem Dagar, Dagar, Prem, Mahendra K. Verma +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #20C30 #20C33 #20G05 #46F10 #47A67 #Advanced Algebra and Geometry #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Microtubule and mitosis dynamics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2405.06450

openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that, for an equivalence class of irreducible smooth representations of the symplectic group Sp(2n,F) over a non-Archimedean local field F, the Jacquet functor with respect to the maximal Levi subgroup GL(l,F)× Sp(2n-2l,F) is multiplicity-free. The proof is based on an explicit computation of Jacquet modules for a broader family of Sp(2n,F)-representations induced from segments, yielding a detailed structural description that may be of independent interest.

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