Non-abelian base change for symmetric power liftings of holomorphic modular forms

TL;DR

This paper proves new cases of Langlands functoriality by establishing the existence of base change liftings for symmetric power automorphic representations of non-CM Hecke eigenforms over totally real fields.

Contribution

It provides a novel proof of base change for symmetric power liftings of automorphic representations associated to non-CM holomorphic modular forms.

Findings

Established base change liftings for symmetric powers over totally real fields.

Extended Langlands functoriality to new cases involving non-CM forms.

Provided a new proof technique for functoriality results.

Abstract

Let $f$ be a non-CM Hecke eigenform of weight $k \geq 2$. We give a new proof of some cases of Langlands functoriality for the automorphic representation $\pi$ associated to $f$. More precisely, we prove the existence of the base change lifting, with respect to any totally real extension $F / \mathbb{Q}$, of any symmetric power lifting of $\pi$.