Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions
Given a holomorphic C₂-cofinite vertex operator algebra V with graded dimension j−744, Borcherds's proof of the monstrous moonshine conjecture implies any finite order automorphism of V has graded trace given by a "completely replicable function", and by work of Cummins and Gannon, th...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209843 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions / S. Carnahan, T. Komuro, S. Urano // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862660147017416704 |
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| author | Carnahan, S. Komuro, T. Urano, S. |
| author_facet | Carnahan, S. Komuro, T. Urano, S. |
| citation_txt | Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions / S. Carnahan, T. Komuro, S. Urano // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Given a holomorphic C₂-cofinite vertex operator algebra V with graded dimension j−744, Borcherds's proof of the monstrous moonshine conjecture implies any finite order automorphism of V has graded trace given by a "completely replicable function", and by work of Cummins and Gannon, these functions are principal moduli of genus zero modular groups. The action of the monster simple group on the monster vertex operator algebra produces 171 such functions, known as the monstrous moonshine functions. We show that 154 of the 157 non-monstrous completely replicable functions cannot possibly occur as trace functions on V.
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| first_indexed | 2025-12-07T15:02:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209843 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:02:44Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Carnahan, S. Komuro, T. Urano, S. 2025-11-27T14:49:19Z 2018 Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions / S. Carnahan, T. Komuro, S. Urano // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 11F22; 17B69 arXiv: 1712.10160 https://nasplib.isofts.kiev.ua/handle/123456789/209843 https://doi.org/10.3842/SIGMA.2018.114 Given a holomorphic C₂-cofinite vertex operator algebra V with graded dimension j−744, Borcherds's proof of the monstrous moonshine conjecture implies any finite order automorphism of V has graded trace given by a "completely replicable function", and by work of Cummins and Gannon, these functions are principal moduli of genus zero modular groups. The action of the monster simple group on the monster vertex operator algebra produces 171 such functions, known as the monstrous moonshine functions. We show that 154 of the 157 non-monstrous completely replicable functions cannot possibly occur as trace functions on V. This research was funded by JSPS Kakenhi Grant-in-Aid for Young Scientists (B) 17K14152. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions Article published earlier |
| spellingShingle | Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions Carnahan, S. Komuro, T. Urano, S. |
| title | Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions |
| title_full | Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions |
| title_fullStr | Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions |
| title_full_unstemmed | Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions |
| title_short | Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions |
| title_sort | characterizing moonshine functions by vertex-operator-algebraic conditions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209843 |
| work_keys_str_mv | AT carnahans characterizingmoonshinefunctionsbyvertexoperatoralgebraicconditions AT komurot characterizingmoonshinefunctionsbyvertexoperatoralgebraicconditions AT uranos characterizingmoonshinefunctionsbyvertexoperatoralgebraicconditions |