An irreducibility result in non-zero characteristic
type: Item
instance of: scholarly article
title: An irreducibility result in non-zero characteristic
zbMATH Open document ID: 1064.22003
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2005-04-15T00:00:00Z
review text: The purpose of this paper is to prove that if \(F\) is a non-archimedean local field and \(G\) is an inner twist of \(GL_n/F,\) then a representation of \(G(F)\) parabolically induced from a square-integrable representation is irreducible. In the case of zero characteristic this was proved by \textit{J. N. Bernstein, P. Deligne, D. A. Kazhdan} and \textit{M.-F. Vignéras} [Représentations des groupes réductifs sur un corps local (1984; Zbl 0583.22009), Theorem B.2.d]. The present paper gives a new proof in the characteristic zero case and a proof in the case of positive characteristic. Novel aspects of the proofs are the reduction of the question of irreducibility to one about orbital integrals using the Paley-Wiener theorem of \textit{J. Bernstein, P. Deligne} and \textit{D. A. Kazhdan} [J. Anal. Math. 47, 180--192 (1986; Zbl 0634.22011)] and Kazhdan's (and Krasner's) theory of close local fields described in an article of P. Deligne in the book referred to above.
reviewed by: Samuel James Patterson
Mathematics Subject Classification ID: 22E35
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G25
Mathematics Subject Classification ID: 20G30
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 2157246
zbMATH Keywords: induced representations
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: Paley-Wiener theorem
zbMATH Keywords: orbital integrals
zbMATH Keywords: close local fields
zbMATH Keywords: square-integrable representations
author: Alexandru Ioan Badulescu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113246752
OpenAlex ID: W2083072662
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DOI: 10.2748/TMJ/1113246752
description: scientific article; zbMATH DE number 2157246