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arXiv · 2405.06450

On the Jacquet functor of Symplectic groups

Prem Dagar·Mahendra Kumar Verma
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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)\times 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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Prem Dagar, Mahendra Kumar Verma. 2026-06-16. On the Jacquet functor of Symplectic groups. https://arxiv.org/abs/2405.06450

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