On Certain Global Constructions of Automorphic Forms Related to Small Representations of $F_4$

TL;DR

This paper explores global constructions of automorphic forms related to small representations of the exceptional group F_4, using integral methods involving minimal representations and unipotent orbits.

Contribution

It introduces new integral constructions for automorphic representations of F_4, connecting minimal representations and unipotent orbit-based descent methods.

Findings

Constructed liftings of automorphic representations in F_4

Developed integral formulas involving minimal representations

Analyzed automorphic forms related to unipotent orbits

Abstract

In this paper we consider some global constructions of liftings of automorphic representations attached to some commuting pairs in the exceptional group $F_4$. We consider two families of integrals. The first uses the minimal representation on the double cover of $F_4$, and in the second we consider examples of integrals of descent type associated with unipotent orbits of $F_4$.