Vertex Operator Algebras Associated to TypeGAffine Lie Algebras II

We continue the study of the vertex operator algebra L(k, 0) associated to a type affine Lie algebra at admissible one-third integer levels, , initiated in Axtell and Lee [3]. We show there are only finitely many irreducible L(k, 0)-modules from the category 𝒪. The proof relies on knowledge of an explicit formula for the singular vectors. After obtaining this formula, we are able to prove there are only finitely many irreducible A(L(k, 0))-modules from the category 𝒪. The main result then follows from the bijective correspondence in A(V)-theory.