Jacquet modules of 𝑝-adic general linear groups

Abstract

In this paper, we study Jacquet modules for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -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.