Global liftings between inner forms of GSp(4)

TL;DR

This paper investigates automorphic liftings between inner forms of GSp(4), establishing the existence of certain global liftings and confirming conjectures about paramodular newforms of squarefree level.

Contribution

It proves the existence of cohomological nontrivial weak global liftings for inner forms of GSp(4) and addresses conjectures on paramodular newforms, providing finer local lifting details.

Findings

Existence of cohomological weak global liftings in many cases

Confirmation of Ibukiyama and Kitayama's conjectures on paramodular newforms

Detailed analysis of local liftings at ramified places for GSp(4) inner forms

Abstract

For reductive groups $G$ over a number field we discuss automorphic liftings from cuspidal irreducible automorphic representations $\pi$ of $G(\mathbb{A})$ to cuspidal irreducible automorphic representations on $H(\mathbb{A})$ for the quasi-split inner form $H$ of $G$. We show the existence of cohomological nontrivial weak global liftings in many cases. A priori these weak liftings do not give a description of the precise nature of the corresponding local liftings at the ramified places and in particular do not characterize the image of the lift. For inner forms of the group $H=\mathrm{GSp}(4)$ however we address these finer details. Especially, we prove the recent conjectures of Ibukiyama and Kitayama on paramodular newforms of squarefree level.