The local theta correspondence for unramified unitary groups
type: Item
instance of: scholarly article
title: The local theta correspondence for unramified unitary groups
zbMATH Open document ID: 0842.11022
DOI: 10.1007/BF02762091
author: Takao Watanabe
published in: Israel Journal of Mathematics
publication date: 1996-07-28T00:00:00Z
review text: Let \(F\) be a non-archimedean local field. The author considers the dual reductive pair \((U_{2n}, U_{2n+1})\) over \(F\) where \(U_{2n}\) and \(U_{2n+1}\) are quasisplit unitary groups over \(F\). The purpose of this paper is to determine the image of the theta correspondence from \(U_{2n}\) to \(U_{2n+1}\) and from \(U_{2n+1}\) to \(U_{2n+2}\). The author computes the correspondence explicitly for spherical representations in these two cases.
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 836176
zbMATH Keywords: dual reductive pair
zbMATH Keywords: quasisplit unitary groups
zbMATH Keywords: image of the theta correspondence
zbMATH Keywords: spherical representations
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
cites work: Q3926803
cites work: \(L\)-functions and Fourier-Jacobi coefficients for the unitary group \(U(3)\)
cites work: Q3856974
cites work: Some results on the unramified principal series of \(p\)-adic groups
cites work: Howe correspondences on a \(p\)-adic field
cites work: Theta liftings for quasi-split unitary groups
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description: scientific article; zbMATH DE number 836176