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

TL;DR

This paper investigates automorphic forms on Sp_4 over the adeles that generate large discrete series representations at the real place, identifying their cuspidal components and structural properties.

Contribution

It characterizes the cuspidal components and structure of automorphic forms associated with large discrete series representations of Sp_4(R).

Findings

Identification of cuspidal components for large discrete series

Structural description of the automorphic form space

Clarification of the relationship between automorphic forms and discrete series

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.