Symmetric power functoriality for Hilbert modular forms

TL;DR

This paper proves the existence of symmetric power liftings for cuspidal automorphic representations linked to Hilbert modular forms over totally real fields, advancing the understanding of automorphic forms and their symmetries.

Contribution

It establishes the existence of symmetric power liftings for Hilbert modular forms, extending functoriality results in the automorphic representation theory.

Findings

Proves existence of symmetric power liftings for Hilbert modular forms.

Extends functoriality principles to totally real fields.

Enhances understanding of automorphic representations and their symmetries.

Abstract

Let $F$ be a totally real field. We prove the existence of all symmetric power liftings of those cuspidal automorphic representations of $\mathrm{GL}_2(\mathbf{A}_F)$ associated to Hilbert modular forms of regular weight.