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

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

1995-09-22

arxiv.org/abs/q-alg/9509025v1

Math. Res. Lett. 2 (1995) 563-575

Mathematics

Quantum Algebra

14 pages, Latex, No Figures, to appear in Mathematical Research Letters, 1995

Scientific paper

We investigate vertex operator algebras $L(k,0)$ associated with
modular-invariant representations for an affine Lie algebra $A_1 ^{(1)}$ ,
where k is '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.

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