On the Jacquet functor of Symplectic groups

Let $\F$ be a non-Archimedean local field.~Consider $\G_{ n}:= \Sp_{ 2n}(\F)$ and let $\M:= \GL_l \times \G_{ n-l}$ be a maximal Levi subgroup of $\G_{ n}$.~This paper undertakes the computation of the Jacquet module of representations of $\G_{ n}$ with respect to the maximal Levi subgroup, belonging to a particular class. Finally, we conclude that for a subclass of representations of $\G_{ n},$ multiplicity of the Jacquet module does not exceed 2.

Categories: math.RT