Hyper-Algebras of Vector-Valued Modular Forms
We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ℚ, acting on these hyper-algebras. These definitions bridge the classical and represent...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209849 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Hyper-Algebras of Vector-Valued Modular Forms / M. Raum // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. |
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Raum, M. 2025-11-27T14:53:25Z 2018 Hyper-Algebras of Vector-Valued Modular Forms / M. Raum // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 11F40; 11F60; 11F70 arXiv: 1810.02048 https://nasplib.isofts.kiev.ua/handle/123456789/209849 https://doi.org/10.3842/SIGMA.2018.108 We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ℚ, acting on these hyper-algebras. These definitions bridge the classical and representation-theoretic approach to Siegel modular forms. Combining both the product structure and the action of Hecke operators, we prove in the case of elliptic modular forms that all cusp forms of sufficiently large weight can be obtained from products involving only two fixed Eisenstein series. As a byproduct, we obtain inclusions of cuspidal automorphic representations into the tensor product of global principal series. The author was partially supported by Vetenskapsrådet Grant 2015-04139. The author is grateful to the referees for various helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hyper-Algebras of Vector-Valued Modular Forms Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Hyper-Algebras of Vector-Valued Modular Forms |
| spellingShingle |
Hyper-Algebras of Vector-Valued Modular Forms Raum, M. |
| title_short |
Hyper-Algebras of Vector-Valued Modular Forms |
| title_full |
Hyper-Algebras of Vector-Valued Modular Forms |
| title_fullStr |
Hyper-Algebras of Vector-Valued Modular Forms |
| title_full_unstemmed |
Hyper-Algebras of Vector-Valued Modular Forms |
| title_sort |
hyper-algebras of vector-valued modular forms |
| author |
Raum, M. |
| author_facet |
Raum, M. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ℚ, acting on these hyper-algebras. These definitions bridge the classical and representation-theoretic approach to Siegel modular forms. Combining both the product structure and the action of Hecke operators, we prove in the case of elliptic modular forms that all cusp forms of sufficiently large weight can be obtained from products involving only two fixed Eisenstein series. As a byproduct, we obtain inclusions of cuspidal automorphic representations into the tensor product of global principal series.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209849 |
| citation_txt |
Hyper-Algebras of Vector-Valued Modular Forms / M. Raum // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. |
| work_keys_str_mv |
AT raumm hyperalgebrasofvectorvaluedmodularforms |
| first_indexed |
2025-12-07T12:29:56Z |
| last_indexed |
2025-12-07T12:29:56Z |
| _version_ |
1850886000914464768 |