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Erschienen in:
2019 | OriginalPaper | Buchkapitel
6. Cuspidal Automorphic Representations Corresponding to Siegel Modular Forms
verfasst von : Ameya Pitale
Erschienen in: Siegel Modular Forms
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Abstract
In this chapter, we start with a cuspidal Hecke eigenform \(F \in S_k(\Gamma _n)\) and construct an irreducible cuspidal automorphic representation of \(\mathrm{GSp}_{2n}({\mathbb A})\) corresponding to it. There are several steps for achieving this— construct a function \(\Phi _F\) on \(\mathrm{GSp}_{2n}({\mathbb A})\) corresponding to F, understand the properties it inherits from F, and study the local components of the representation generated by \(\Phi _F\). The main reference for this chapter is the article [6] by Asgari and Schmidt. We suggest the reader to go over Appendix B and C to refresh the details about adeles and local representation theory of \(\mathrm{GL}_2\).