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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2019 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2019
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210192 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706721033551872 |
|---|---|
| author | Carnahan, S. |
| author_facet | Carnahan, S. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T21:24:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210192 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:41Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | A Self-Dual Integral Form of the Moonshine Module Carnahan, S. |
| title | 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_short | A Self-Dual Integral Form of the Moonshine Module |
| title_sort | self-dual integral form of the moonshine module |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210192 |
| work_keys_str_mv | AT carnahans aselfdualintegralformofthemoonshinemodule AT carnahans selfdualintegralformofthemoonshinemodule |