Vertex operator algebras associated to modular invariant representations for $A_1 ^{(1)}$

We investigate vertex operator algebras $L(k,0)$ associated with modular-invariant representations for an affine Lie algebra $A_1 ^{(1)}$, where k is an`admissible' rational number. We show that VOA $L(k,0)$ is rational in the category $\cal O$ and find all irreducible representations in the category of weight modules.

Full Text (PDF format)

Published 1 January 1995