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

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

1996-05-30

arxiv.org/abs/hep-th/9605220v1

Commun.Math.Phys. 185 (1997) 467-493

Physics

High Energy Physics

High Energy Physics - Theory

Latex file, 31pp, 6 epsf figures uufiled

Scientific paper

10.1007/s002200050099

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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