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arXiv · 2405.05719

A note on Jacquet modules of general linear groups

Prem Dagar·Mahendra Kumar Verma
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Abstract

Let F be a non-Archimedean local field. Consider G_n:= GL_n(F) and let M:= G_l * G_{n-l} be a maximal Levi subgroup of G_n. In this article, we compute the semisimplified Jacquet module of representations of G_n 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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Prem Dagar, Mahendra Kumar Verma. 2024-05-09. A note on Jacquet modules of general linear groups. https://arxiv.org/abs/2405.05719

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