Super dual pairs and highest weight modules of orthosymplectic algebras
type: Item
instance of: scholarly article
title: Super dual pairs and highest weight modules of orthosymplectic algebras
zbMATH Open document ID: 0802.17002
author: Kyo Nishiyama
published in: Advances in Mathematics
publication date: 1994-12-15T00:00:00Z
review text: For a symplectic Lie group \(\text{Sp} (2n,\mathbb{R})\), all unitary lowest (or highest) weight representations can be realized as a subrepresentation in some power of tensor products of the Weil representation (also known as the oscillator representation). In the present paper this result is extended to the orthosymplectic Lie superalgebra \(\text{osp} (2n, m; \mathbb{R})\). A complete result is obtained only for \(\text{osp} (2,2; \mathbb{R})\), but also for the general case interesting results are proved. The method used in this paper is based upon the notion of super dual pairs, following Lie algebra dual pairs of \textit{R. Howe} [Bull. Am. Math. Soc., New Ser. 3, 821-843 (1980; Zbl 0442.43002)].
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 611209
zbMATH Keywords: unitary representations
zbMATH Keywords: oscillator representation
zbMATH Keywords: orthosymplectic Lie superalgebra \(\text{osp} (2n, m
zbMATH Keywords: \mathbb{R})\)
zbMATH Keywords: super dual pairs
MaRDI profile type: Publication
full work available at URL: aima.1994.1021
OpenAlex ID: W1973922123
DOI: 10.1006/AIMA.1994.1021
description: scientific article; zbMATH DE number 611209