Jacquet modules of 𝑝-adic general linear groups

Jantzen, Chris

doi:10.1090/S1088-4165-07-00316-0

Jacquet modules of $p$-adic general linear groups
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by Chris Jantzen

Represent. Theory 11 (2007), 45-83

DOI: https://doi.org/10.1090/S1088-4165-07-00316-0

Published electronically: April 18, 2007

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Abstract:

In this paper, we study Jacquet modules for $p$-adic general linear groups. More precisely, we have results—formulas and algorithms—aimed at addressing the following question: Given the Langlands data for an irreducible representation, can we determine its (semisimplified) Jacquet module? We use our results to answer this question in a number of cases, as well as to recover some familiar results as relatively easy consequences.

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