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| _version_ | 1862537294111571968 |
|---|---|
| author | Franc, Cameron Mason, Geoffrey |
| author_facet | Franc, Cameron Mason, Geoffrey |
| citation_txt | Character Vectors of Strongly Regular Vertex Operator Algebras. Cameron Franc and Geoffrey Mason. SIGMA 18 (2022), 085, 49 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-12T17:11:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211819 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T17:11:27Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Franc, Cameron Mason, Geoffrey 2026-01-12T10:18:46Z 2022 Character Vectors of Strongly Regular Vertex Operator Algebras. Cameron Franc and Geoffrey Mason. SIGMA 18 (2022), 085, 49 pages 1815-0659 2020 Mathematics Subject Classification: 17B69; 18M20; 11F03 arXiv:2111.04616 https://nasplib.isofts.kiev.ua/handle/123456789/211819 https://doi.org/10.3842/SIGMA.2022.085 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. Franc was supported by an NSERC Discovery Grant, and Mason was supported by grant #427007 from the Simons Foundation. We thank these institutions for their support. We also thank the anonymous referees for their helpful comments on an earlier draft of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Character Vectors of Strongly Regular Vertex Operator Algebras Article published earlier |
| spellingShingle | Character Vectors of Strongly Regular Vertex Operator Algebras Franc, Cameron Mason, Geoffrey |
| title | Character Vectors of Strongly Regular Vertex Operator Algebras |
| title_full | Character Vectors of Strongly Regular Vertex Operator Algebras |
| title_fullStr | Character Vectors of Strongly Regular Vertex Operator Algebras |
| title_full_unstemmed | Character Vectors of Strongly Regular Vertex Operator Algebras |
| title_short | Character Vectors of Strongly Regular Vertex Operator Algebras |
| title_sort | character vectors of strongly regular vertex operator algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211819 |
| work_keys_str_mv | AT franccameron charactervectorsofstronglyregularvertexoperatoralgebras AT masongeoffrey charactervectorsofstronglyregularvertexoperatoralgebras |