and as Vertex Operator Extensionsof Dual Affine Algebras
Abstract
We discover a realisation of the affine Lie superalgebra and of the exceptional affine superalgebra as vertex operator extensions of two algebras with ``dual'' levels (and an auxiliary level1 algebra). The duality relation between the levels is . We construct the representation of on a sum of tensor products of , , and modules and decompose it into a direct sum over the spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to is traced to the properties of embeddings into and their relation with the dual pairs. Conversely, we show how the representations are constructed from representations.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2000
 DOI:
 10.1007/PL00005536
 arXiv:
 arXiv:hepth/9907171
 Bibcode:
 2000CMaPh.214..495B
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Representation Theory
 EPrint:
 50 pages, Latex2e, 2 figures, acknowledgements added