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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2018
Hauptverfasser: Carnahan, S., Komuro, T., Urano, S.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2018
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/209843
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
id nasplib_isofts_kiev_ua-123456789-209843
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions
spellingShingle Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions
Carnahan, S.
Komuro, T.
Urano, S.
title_short 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_sort characterizing moonshine functions by vertex-operator-algebraic conditions
author Carnahan, S.
Komuro, T.
Urano, S.
author_facet Carnahan, S.
Komuro, T.
Urano, S.
publishDate 2018
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/209843
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.
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AT komurot characterizingmoonshinefunctionsbyvertexoperatoralgebraicconditions
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first_indexed 2025-12-07T15:02:44Z
last_indexed 2025-12-07T15:02:44Z
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