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A construction of the \(c<1\) modular invariant partition functions. (English) Zbl 0661.17019

In a previous paper [K. Bardakci, E. Rabinovici and B. Säring, Nucl. Phys. B 299, No.1, 151-182 (1988; Zbl 0661.17018)], two- dimensional conformal field theories, i.e. unitary representations of the direct sum of two copies of the Virasoro algebra, were constructed by tensoring discrete series representations. It was shown that all the models of types A and D can be obtained in this way [for the classification of such models, see A. Cappelli, C. Itzykson and J.-B. Zuber, Modular invariant partition functions in two dimensions, Nucl. Phys. B 280, 445-465 (1987; Zbl 0661.17017)].
The present paper shows that the exceptional E types can also be obtained. It also proves a result which describes the decomposition of the restriction of the four spin representations of the affine algebra of \({\mathfrak o}(4n)\) to a certain subalgebra, which is used in the coset construction of the discrete series representations [P. Goddard, A. Kent and D. Olive, Phys. Lett. B 152, 88-92 (1985; Zbl 0661.17015)].
Reviewer: A.N.Pressley

MSC:

17B65 Infinite-dimensional Lie (super)algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
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