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| Summary: | 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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| ISSN: | 1815-0659 |