\(L^ 2\)-versions of the Howe correspondence. II
type: Item
instance of: scholarly article
title: \(L^ 2\)-versions of the Howe correspondence. II
zbMATH Open document ID: 0844.22020
author: Genkai Zhang
author: Bent Ørsted
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1996-08-26T00:00:00Z
review text: [Part I of this paper will appear in Math. Scand.] We present the explicit decomposition of the space of \(L^2\)-sections of vector bundles over the projective complex and quaternion hyperboloids. Using this we further calculate the \(L^2\) decompositions of the metaplectic representations for the dual pairs \(SL (2, \mathbb{R}) \times O(p,q)\), \(U(1,1) \times U (p,q)\) and \(O^* (4) \times Sp (p,q)\) by extending the idea of pluriharmonic functions due to M. Kashiwara and M. Vergne.
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 891038
zbMATH Keywords: \(L^ 2\)-sections
zbMATH Keywords: decomposition
zbMATH Keywords: vector bundles
zbMATH Keywords: hyperboloids
zbMATH Keywords: metaplectic representations
zbMATH Keywords: pluriharmonic functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 891038