A note on Jacquet modules of general linear groups
Abstract
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 article, we compute the semisimplified 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.
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