A note on Jacquet modules of general linear groups

Prem Dagar; Mahendra Kumar Verma

doi:10.1142/S021949882650074X

A note on Jacquet modules of general linear groups

Prem Dagar, Mahendra Kumar Verma

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	English
Article number	2650074
Journal	Journal of Algebra and its Applications
DOIs	https://doi.org/10.1142/S021949882650074X
State	Accepted/In press - 1 Jan 2024
Externally published	Yes

Keywords

General linear groups
Jacquet modules
multiplicity free representations

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1142/S021949882650074X

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AB - 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.

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A note on Jacquet modules of general linear groups

Abstract

Keywords

ASJC Scopus subject areas

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