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
Datum:2018
1. Verfasser: Raum, M.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2018
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung: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