Hyper-Algebras of Vector-Valued Modular Forms
Artikel i vetenskaplig tidskrift, 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

Författare

Martin Raum

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Symmetry, Integrability and Geometry - Methods and Applications

1815-0659 (ISSN)

Vol. 14 108

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

Fundament

Grundläggande vetenskaper

DOI

10.3842/SIGMA.2018.108

Mer information

Senast uppdaterat

2018-12-16