Cuspidal components of Siegel modular forms for large discrete series representations of $\mathrm{Sp}_4(\mathbb{R})$

Shuji Horinaga; Hiro-aki Narita

Cuspidal components of Siegel modular forms for large discrete series representations of $\mathrm{Sp}_4(\mathbb{R})$

Number Theory 2023-01-30 v1

Authors: Shuji Horinaga , Hiro-aki Narita

Abstract

In this paper, we consider automorphic forms on $\mathrm{Sp}_4(\mathbb{A}_\mathbb{Q})$ which generate large discrete series representations of $\mathrm{Sp}_4(\mathbb{R})$ as $(\mathfrak{sp}_4(\mathbb{R}),K_\infty)$ -modules. We determine the cuspidal components and the structure of the space of such automorphic forms.

Keywords

siegel modular forms automorphic forms large discrete series sp_4 cuspidal components

Cite

@article{arxiv.2301.11552,
  title  = {Cuspidal components of Siegel modular forms for large discrete series representations of $\mathrm{Sp}_4(\mathbb{R})$},
  author = {Shuji Horinaga and Hiro-aki Narita},
  journal= {arXiv preprint arXiv:2301.11552},
  year   = {2023}
}

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