Unitary representations of basic classical Lie superalgebras
type: Item
instance of: scholarly article
title: Unitary representations of basic classical Lie superalgebras
zbMATH Open document ID: 0715.17027
DOI: 10.1007/BF00398365
published in: Letters in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: Among the basic classical Lie superalgebras, gl(m/n) and C(n) are the only ones admitting finite-dimensional unitary irreducible representations; these unitary representations are sometimes called the star representations [\textit{M. Scheunert}, \textit{W. Nahm} and \textit{V. Rittenberg}, J. Math. Phys. 18, 146-154 (1977; Zbl 0354.17004)]. In this paper, the necessary and sufficient conditions on the highest weight \(\Lambda\) of a finite-dimensional simple module V(\(\Lambda\)) are given for V(\(\Lambda\)) to be unitary. The lowest weights of such unitary irreducible representations can be worked out explicitly (even in the case when V(\(\Lambda\)) is atypical). The covariant, resp. contravariant, tensor representations of gl(m/n), appearing in the tensor product of the standard gl(m/n) module (resp. the dual of the standard module), are shown to be unitary.
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17A70
zbMATH DE Number: 4177344
zbMATH Keywords: classical Lie superalgebras
zbMATH Keywords: unitary irreducible representations
zbMATH Keywords: star representations
zbMATH Keywords: highest weight
zbMATH Keywords: atypical
zbMATH Keywords: covariant
zbMATH Keywords: contravariant
zbMATH Keywords: tensor representations
author: Mark D. Gould
author: R. B. Zhang
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00398365
OpenAlex ID: W2053555631
description: scientific article; zbMATH DE number 4177344