On the Jacquet functor of Symplectic groups

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.