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Zbl 0854.17034
Zhu, Yongchang
Modular invariance of characters of vertex operator algebras. (English)
[J] J. Am. Math. Soc. 9, No. 1, 237-302 (1996). ISSN 0894-0347; ISSN 1088-6834/e

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.
[Xu Xiaoping (Kowloon)]

MSC 2000:: *17B69 Vertex operators
11F22 Relationship of automorphic forms to Lie algebras, etc.
17B68 Virasoro and related algebras

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

Cited in: Zbl 1233.17021 Zbl 1230.17019 Zbl 1214.81243 Zbl 1232.17038 Zbl 1204.81155 Zbl 1211.17026 Zbl 1186.17011 Zbl 1163.17029 Zbl 1145.17010 Zbl 1147.11025 Zbl 1146.11026 Zbl 1133.17016 Zbl 1129.17015 Zbl 1124.11022 Zbl 1165.17311 Zbl 1100.17010 Zbl 1020.17020 Zbl 1037.17032 Zbl 1017.17026 Zbl 0990.17022 Zbl 1002.17016 Zbl 0976.81091 Zbl 0953.17017 Zbl 0911.17017 Zbl 0890.17029 Zbl 0890.17030

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