On the group-theoretical approach to extended conformal supersymmetry: classification of multiplets
type: Item
instance of: scholarly article
title: On the group-theoretical approach to extended conformal supersymmetry: classification of multiplets
zbMATH Open document ID: 0585.17003
DOI: 10.1007/BF00397755
published in: Letters in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: The authors investigate a certain physically interesting class of infinite-dimensional reducible but indecomposable representations of the conformal Lie superalgebra \(su(2,2/N)\) (a real form of \(sl(4/N,\mathbb C)\) whose Lie algebra is the direct product of \(su(2,2)\), \(su(N)\), and a one-dimensional centre). An elementary representation is defined to be induced from a finite-dimensional representation of a suitable parabolic subalgebra of \(su(2,2/N)\). All these representations can be regarded as lowest weight representations of \(sl(4/N,\mathbb C)\). A multiplet is a set \(M\) of elementary representations such that: 1) For any \(R\in M\), the set of all elementary representations which are partially equivalent to but different from \(R\) is non-empty and contained in \(M\). 2) \(M\) does not contain any proper non-empty subset for which 1) is satisfied. The authors display the conditions for reducibility of the elementary representations and present a major part of their classification of the multiplets (which includes the specification of the elementary representations contained in any type of multiplet).
reviewed by: M. Scheunert
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 81T60
zbMATH DE Number: 3937360
zbMATH Keywords: superfields
zbMATH Keywords: infinite-dimensional representation
zbMATH Keywords: infinite-dimensional induced representation
zbMATH Keywords: infinite-dimensional
zbMATH Keywords: indecomposable representation
zbMATH Keywords: conformal Lie superalgebra
zbMATH Keywords: multiplet
author: V. K. Dobrev
author: Valentina B. Petkova
MaRDI profile type: Publication
cites work: Elementary representations and intertwining operators for the group SU*(4)
cites work: The six-point families of exceptional representations of the conformal group
cites work: Representations of conformal supersymmetry
cites work: \(N=1\) superconformal tensor calculus. Multiplets with external Lorentz indices and derivative operations
full work available at URL: https://doi.org/10.1007/bf00397755
OpenAlex ID: W1983587920
description: scientific article; zbMATH DE number 3937360