A note on Jacquet modules of general linear groups.

Let F be a non-Archimedean local field. Consider Gn := GLn(F) and let M := Gl ×Gn−l be a maximal Levi subgroup of Gn. In this paper, we compute the semi simplified Jacquet module of representations of Gn with respect to the maximal Levi subgroup M, belonging to a particular category of representations. Utilizing our results, we prove that the Jacquet module is multiplicity-free for a specific subcategory of representations. Our findings are based on the Zelevinsky classification. [ABSTRACT FROM AUTHOR]