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arXiv · hep-th/9605220

Representation theory of the affine Lie superalgebra sl(2|1) at fractional level

P. Bowcock·A. Taormina
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Abstract

N=2 noncritical strings are closely related to the $\Slr/\Slr$ Wess-Zumino- Novikov-Witten model, and there is much hope to further probe the former by using the algebraic apparatus provided by the latter. An important ingredient is the precise knowledge of the $\hslc$ representation theory at fractional level. In this paper, the embedding diagrams of singular vectors appearing in $\hslc$ Verma modules for fractional values of the level ($k=p/q-1$, p and q coprime) are derived analytically. The nilpotency of the fermionic generators in $\hslc$ requires the introduction of a nontrivial generalisation of the MFF construction to relate singular vectors among themselves. The diagrams reveal a striking similarity with the degenerate representations of the $N=2$ superconformal algebra.

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P. Bowcock, A. Taormina. 1996-05-30. Representation theory of the affine Lie superalgebra sl(2|1) at fractional level. https://doi.org/10.1007/s002200050099

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