Theta lifting of cusp forms on the unitary group \(U(d, d)\)
type: Item
instance of: scholarly article
title: Theta lifting of cusp forms on the unitary group \(U(d, d)\)
zbMATH Open document ID: 0768.11018
DOI: 10.1215/S0012-7094-92-06706-8
author: Takao Watanabe
published in: Duke Mathematical Journal
publication date: 1992-12-14T00:00:00Z
review text: This paper studies some fundamental problems for the theta lifting for unitary groups over a totally imaginary quadratic extension of a totally real number field. After a discussion of the structure of quasi-split unitary groups, the author computes the Fourier coefficients of the theta lifting. A main result of the paper is the following theorem: If an irreducible nontrivial cuspidal representation of \(U(d,d)\) admits a Whittaker model, its theta lifting to \(U(n,n)\) is nonzero when \(n > d\); further, the theta lifting is not cuspidal when \(n > d+1\).
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 22E55
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 78555
zbMATH Keywords: theta lifting
zbMATH Keywords: unitary groups
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: cuspidal representation
zbMATH Keywords: Whittaker model
reviewed by: Yangbo Ye
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 78555