On the group-theoretical approach to extended conformal supersymmetry: classification of multiplets
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).
infinite-dimensional induced representation
scientific article; zbMATH DE number 3937360