Nonvanishing of a certain sesquilinear form in the theta correspondence
type: Item
instance of: scholarly article
zbMATH Open document ID: 0993.22011
author: Hongyu He
publication date: 2001-12-17T00:00:00Z
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 1683067
zbMATH Keywords: dual pair
zbMATH Keywords: metaplectic representation
zbMATH Keywords: Harish-Chandra module
MaRDI profile type: Publication
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title: Nonvanishing of a certain sesquilinear form in the theta correspondence
published in: Representation Theory
review text: In his paper [Commun. Contemp. Math. 2, 255-283 (2000; Zbl 0951.22008)], the author studied a certain sesquilinear form \((\;,\;)_\pi\) (introduced by Jian-Shu Li in 1989) for \(\pi\) in the semistable range of \(\theta(MO(p,q))\rightarrow MSp_{2n}(\mathbb{R})\), \(p+q\leq 2n+1\). In the paper under review the author shows that either \((\;,\;)_\pi\) or \((\;,\;)_{\pi\otimes \det}\) is nonvanishing. These results combined with a result of Przebinda suggest the existence of certain unipotent representations of \(Mp_{2n}(\mathbb{R})\) beyond the unitary representations of low rank.
reviewed by: Vladimir L. Popov
description: scientific article; zbMATH DE number 1683067