Modular invariance of characters of vertex operator algebras. (English) Zbl 0854.17034

Zhu, Yongchang

J. Am. Math. Soc. 9, No. 1, 237-302 (1996).

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.

Reviewer: Xu Xiaoping (Kowloon)

MSC:

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

Keywords:

conformal blocks; traces; modular invariance; characters of irreducible representations; vertex operator algebra

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