Hyper-Algebras of Vector-Valued Modular Forms
Journal article, 2018

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.

vector-valued Hecke operators

automorphic representations

Siegel modular forms

Author

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Symmetry, Integrability and Geometry - Methods and Applications

1815-0659 (ISSN)

Vol. 14 108

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

Roots

Basic sciences

DOI

10.3842/SIGMA.2018.108

More information

Latest update

3/19/2019