On Zhu's Associative Algebra as a Tool in the Representation Theory of Vertex Operator Algebras

Details On Zhu's Associative Algebra as a Tool in the Representation Theory of Vertex Operator Algebras On Zhu's Associative Algebra as a Tool in the Representation Theory of Vertex Operator Algebras

1996-05-03

arxiv.org/abs/hep-th/9605020v1

Physics

High Energy Physics

High Energy Physics - Theory

60 pages, Latex

Scientific paper

We describe an approach to classify (meromorphic) representations of a given vertex operator algebra by calculating Zhu's algebra explicitly. We demonstrate this for FKS lattice theories and subtheories corresponding to the Z_2 reflection twist and the Z_3 twist. Our work is mainly offering a novel uniqueness tool, but, as shown in the Z_3 case, it can also be used to extract enough information to construct new representations. We prove the existence and some properties of a new non-unitary representation of the Z_3-invariant subtheory of the (two dimensional) Heisenberg algebra.

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