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Level one representations of the simple affine Kac-Moody algebras in their homogeneous gradations

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Abstract

Using the central charge of the Virasoro algebra as a clue, we recall the known constructions of theA, D, E algebras and discuss new Bosonic constructions of the non simply laced affine Kac-Moody algebras: the twistedA, D, E and theB, C, F, andG algebras. These involve interacting Fermions and a generalization of the Frenkel-Kac sign operators which do not form a 2-cocycle when the horizontal algebra has more than one short simple root.

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  1. Jean Thierry-Mieg

    Present address: DAMTP, Silver Street, Cambridge, England

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  1. Groupe d'Astrophysique Relativiste, CNRS, Observatoire de Paris-Meudon, F-92195, Meudon, France

    Denis Bernard & Jean Thierry-Mieg

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  1. Denis Bernard
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Communicated by A. Jaffe

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Bernard, D., Thierry-Mieg, J. Level one representations of the simple affine Kac-Moody algebras in their homogeneous gradations. Commun.Math. Phys. 111, 181–246 (1987). https://doi.org/10.1007/BF01217760

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