A Self-Dual Integral Form of the Moonshine Module
We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the proof of the modular moonshine conjecture by Borcherds and...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210192 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Self-Dual Integral Form of the Moonshine Module / S. Carnahan // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 48 назв. — англ. |
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Carnahan, S. 2025-12-03T14:33:50Z 2019 A Self-Dual Integral Form of the Moonshine Module / S. Carnahan // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 48 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B69; 11F22; 20C10; 20C20; 20C34 arXiv: 1710.00737 https://nasplib.isofts.kiev.ua/handle/123456789/210192 https://doi.org/10.3842/SIGMA.2019.030 We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the proof of the modular moonshine conjecture by Borcherds and Ryba. As a corollary, we find that Griess's original 196884-dimensional representation of the monster admits a positive-definite self-dual integral form with monster symmetry. I would like to thank Toshiyuki Abe for describing the constructions in [1] in detail at the "VOA and related topics" workshop at Osaka University in March 2017. I would also like to thank the anonymous referees for many helpful comments, and one referee in particular for their help with the proof of Lemma 2.13. This research was partly funded by JSPS Kakenhi Grant-in-Aid for Young Scientists (B) 17K14152. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Self-Dual Integral Form of the Moonshine Module Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A Self-Dual Integral Form of the Moonshine Module |
| spellingShingle |
A Self-Dual Integral Form of the Moonshine Module Carnahan, S. |
| title_short |
A Self-Dual Integral Form of the Moonshine Module |
| title_full |
A Self-Dual Integral Form of the Moonshine Module |
| title_fullStr |
A Self-Dual Integral Form of the Moonshine Module |
| title_full_unstemmed |
A Self-Dual Integral Form of the Moonshine Module |
| title_sort |
self-dual integral form of the moonshine module |
| author |
Carnahan, S. |
| author_facet |
Carnahan, S. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the proof of the modular moonshine conjecture by Borcherds and Ryba. As a corollary, we find that Griess's original 196884-dimensional representation of the monster admits a positive-definite self-dual integral form with monster symmetry.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210192 |
| citation_txt |
A Self-Dual Integral Form of the Moonshine Module / S. Carnahan // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 48 назв. — англ. |
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AT carnahans aselfdualintegralformofthemoonshinemodule AT carnahans selfdualintegralformofthemoonshinemodule |
| first_indexed |
2025-12-07T21:24:41Z |
| last_indexed |
2025-12-07T21:24:41Z |
| _version_ |
1850886252566413312 |