Hyper-Algebras of Vector-Valued Modular Forms

Abstract : 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.
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Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01289143
Contributeur : Martin Westerholt-Raum <>
Soumis le : mercredi 16 mars 2016 - 15:37:24
Dernière modification le : vendredi 18 mars 2016 - 01:02:25
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Martin Westerholt-Raum. Hyper-Algebras of Vector-Valued Modular Forms. 2016. <hal-01289143>

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