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

Antun Milas; Drazen Adamovic

arxiv: q-alg/9509025 · v1 · submitted 1995-09-22 · q-alg · math.QA

Vertex operator algebras associated to modular invariant representations for A₁ ⁽¹⁾

Drazen Adamovic , Antun Milas This is my paper

classification q-alg math.QA

keywords representationsalgebrasassociatedcategoryoperatorrationalvertexadmissible

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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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Reduction and inverse-reduction functors I: standard $\mathsf{V^k}(\mathfrak{sl}_2)$-modules
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The paper develops a formalism for reduction and inverse-reduction functors and computes the action of reduction on standard modules of V^k(sl_2), noting unbounded spectral sequences.