Lowest weight modules of \(\widetilde{\mathrm{Sp}_{2n}(\mathbb R)}\) of minimal Gelfand-Kirillov dimension
type: Item
instance of: scholarly article
title: Lowest weight modules of \(\widetilde{\mathrm{Sp}_{2n}(\mathbb R)}\) of minimal Gelfand-Kirillov dimension
zbMATH Open document ID: 1148.22015
author: Binyong Sun
published in: Journal of Algebra
publication date: 2008-05-21T00:00:00Z
review text: This paper gives a classification of the irreducible lowest weight modules of the metaplectic group with Gelfand-Kirillov dimension \(n\). It is known that there are only four unitary ones with Gelfand-Kirillov dimension \(n\), also known as the minimal representations, namely, the two irreducible constituents of the oscillator representation and their duals. The main result is a criterion on the lowest weights for which the corresponding module is of GK dimension \(n\). It is also proved that these modules occur as submodules of the oscillator representation tensoring with a finite dimensional representation in the sense of Zuckerman.
Mathematics Subject Classification ID: 22E55
zbMATH DE Number: 5277628
zbMATH Keywords: lowest weight module
zbMATH Keywords: Gelfand-Kirillov dimension
zbMATH Keywords: oscillator representation
zbMATH Keywords: metaplectic group
reviewed by: Hongyu He
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2007.05.022
OpenAlex ID: W2362430666
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DOI: 10.1016/J.JALGEBRA.2007.05.022
description: scientific article; zbMATH DE number 5277628