Reductive dual pair correspondence for complex groups
type: Item
instance of: scholarly article
title: Reductive dual pair correspondence for complex groups
zbMATH Open document ID: 0841.22014
author: Dan Barbasch
author: Jeffrey Adams
published in: Journal of Functional Analysis
publication date: 1995-08-27T00:00:00Z
review text: The authors give an explicit determination of the representation correspondence for complex reductive dual pairs \(G_1\), \(G_2\). The case of orthogonal/symplectic pairs over \(\mathbb{R}\) was treated by \textit{C. Moeglin} [ibid. 85, 1-85 (1989; Zbl 0729.22017)]. She first determined the correspondence for certain basic cases, which are discrete series in which the minimal \(K\)-type is also degree-lowest, and then used the induction principle to extend the results to a large class of representations. The authors treat the complex case by using one-dimensional representations of \(G_1\) for the basic set instead of the discrete series, and obtain the full correspondence from the one for the basic cases by application of the induction principle.
reviewed by: Min Ho Lee
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 790373
zbMATH Keywords: theta-correspondences
zbMATH Keywords: oscillator representations
zbMATH Keywords: \(K\)-type
zbMATH Keywords: orthogonal pairs
zbMATH Keywords: symplectic pairs
zbMATH Keywords: representation
zbMATH Keywords: complex reductive dual pairs
MaRDI profile type: Publication
full work available at URL: jfan.1995.1099
OpenAlex ID: W2055009585
DOI: 10.1006/JFAN.1995.1099
description: scientific article; zbMATH DE number 790373