The local theta correspondence of irreducible type 2 dual reductive pairs
type: Item
instance of: scholarly article
title: The local theta correspondence of irreducible type 2 dual reductive pairs
zbMATH Open document ID: 0842.11023
author: Takao Watanabe
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1996-03-18T00:00:00Z
review text: Let \(F\) be a non-archimedean local field. The author considers the dual reductive pair \((\text{GL}_n\), \(\text{GL}_{n+1})\) over \(F\). The purpose of this paper is to determine the image of the theta correspondence from \(\text{GL}_n\) to \(\text{GL}_{n+1}\). The author gives a result in this direction which partially describes the image in terms of the Bernstein-Zelevinsky classification of representations of the general linear groups. The proof involves a delicate local analysis of the Weil representation in this case and in particular makes essential use of the local theory of zeta functions.
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 847739
zbMATH Keywords: dual reductive pair
zbMATH Keywords: image of the theta correspondence
zbMATH Keywords: Bernstein-Zelevinsky classification of representations
zbMATH Keywords: Weil representation
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225459
OpenAlex ID: W2011235673
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DOI: 10.2748/TMJ/1178225459
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description: scientific article; zbMATH DE number 847739