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Vertex operator algebras, generalized doubles and dual pairs

C. Dong·G. Yamskulna
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Abstract

Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let S be a finite set of inequivalent irreducible V-modules which is closed under the action of G. There is a finite dimensional semisimple associative algebra A_α(G,S) for a suitable 2-cocycle αnaturally determined by the G-action on S such that A_α(G,S) and the vertex operator algebra V^G form a dual pair on the sum of V-modules in S in the sense of Howe. In particular, every irreducible V-module is completely reducible V^G-module.

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C. Dong, G. Yamskulna. 2000-06-01. Vertex operator algebras, generalized doubles and dual pairs. https://arxiv.org/abs/math/0006005

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