The genuine omega-regular unitary dual of the metaplectic group
type: Item
instance of: scholarly article
zbMATH Open document ID: 1242.22020
author: Alessandra Pantano
author: Annegret Paul
author: Susana A. Salamanca-Riba
published in: Canadian Journal of Mathematics
publication date: 2012-06-04T00:00:00Z
full work available at URL: CJM-2011-075-x
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 6042743
zbMATH Keywords: metaplectic group
zbMATH Keywords: oscillator representation
zbMATH Keywords: bottom layer map
zbMATH Keywords: cohomological induction
zbMATH Keywords: principal series
MaRDI profile type: Publication
DOI: 10.4153/CJM-2011-075-X
title: The genuine omega-regular unitary dual of the metaplectic group
review text: In this paper the authors classify all genuine unitary representations of the metaplectic group of rank \(n\) whose infinitesimal character is real and at least as regular as that of an oscillator representation. Examples of such representations can be obtained using cohomological induction from tensor products of a one-dimensional representation and an oscillator representation. The main result of the paper asserts that the representations obtained in the latter way are all genuine unitary representations with infinitesimal character as above. The authors also conjecture a similar phenomenon for any double cover of a reductive linear group.
reviewed by: Volodymyr Mazorchuk
description: scientific article; zbMATH DE number 6042743