Character Vectors of Strongly Regular Vertex Operator Algebras
We summarize interactions between vertex operator algebras and number theory through the lens of Zhu theory. The paper begins by recalling basic facts on vertex operator algebras (VOAs) and modular forms, and then explains Zhu's theorem on characters of VOAs in a slightly new form. We then axio...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211819 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Character Vectors of Strongly Regular Vertex Operator Algebras. Cameron Franc and Geoffrey Mason. SIGMA 18 (2022), 085, 49 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We summarize interactions between vertex operator algebras and number theory through the lens of Zhu theory. The paper begins by recalling basic facts on vertex operator algebras (VOAs) and modular forms, and then explains Zhu's theorem on characters of VOAs in a slightly new form. We then axiomatize the desirable properties of modular forms that have played a role in Zhu's theorem and related classification results of VOAs. After this, we summarize known classification results in rank two, emphasizing the geometric theory of vector-valued modular forms as a means for simplifying the discussion. We conclude by summarizing some known examples and by providing some new examples in higher ranks. In particular, the paper contains a number of potential character vectors that could plausibly correspond to a VOA, but the existence of a corresponding hypothetical VOA is presently unknown.
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| ISSN: | 1815-0659 |