Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-07-21
Commun.Math.Phys. 214 (2000) 495-545
Physics
High Energy Physics
High Energy Physics - Theory
50 pages, Latex2e, 2 figures, acknowledgements added
Scientific paper
10.1007/PL00005536
We discover a realisation of the affine Lie superalgebra sl(2|1) and of the exceptional affine superalgebra D(2|1;alpha) as vertex operator extensions of two affine sl(2) algebras with dual levels (and an auxiliary level 1 sl(2) algebra). The duality relation between the levels is (k+1)(k'+1)=1. We construct the representation of sl(2|1) at level k' on a sum of tensor products of sl(2) at level k, sl(2) at level k' and sl(2) at level 1 modules and decompose it into a direct sum over the sl(2|1) spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to the affine D(2|1;k') at level k is traced to properties of sl(2)+sl(2)+sl(2) embeddings into D(2|1;alpha) and their relation with the dual sl(2) pairs. Conversely, we show how the level k' sl(2) representations are constructed from level k sl(2|1) representations.
Bowcock Peter
Feigin B. L.
Taormina Anne
~Semikhatov ~M. A.
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