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Modular invariance of characters of vertex operator algebras. (English) Zbl 0854.17034
The author proves modular invariance of the characters of irreducible representations for a vertex operator algebra under certain finiteness conditions. In order to prove the result, an analogue of highest-weight theory in Lie algebras for vertex operator algebras is developed. Moreover, he proves that a vertex operator algebra allows a certain change-of-variables.

MSC:
17B69 Vertex operators; vertex operator algebras and related structures
11F22 Relationship to Lie algebras and finite simple groups
17B68 Virasoro and related algebras
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