Automorphy of $\mathrm{GL}_2\otimes \mathrm{GL}_n$ in the self-dual case

TL;DR

This paper proves a new case of Langlands functoriality, showing that the tensor product of certain Galois representations and automorphic representations is automorphic under specific conditions, advancing understanding of automorphic forms.

Contribution

It establishes the automorphy of the tensor product of Galois and automorphic representations for GL_2 and GL_n, extending known cases of Langlands functoriality.

Findings

Proves automorphy of tensor products under regularity and irreducibility hypotheses.

Extends Langlands functoriality to new cases involving GL_2 and GL_n.

Provides conditions under which the tensor product is automorphic.

Abstract

In this paper we establish a new case of Langlands functoriality. More precisely, we prove that the tensor product of the compatible system of Galois representations attached to a level-1 classical modular form and the compatible system attached to an n-dimensional RACP automorphic representation of GL_n of the adeles of Q is automorphic, for any positive integer n, under some natural hypotheses (namely regularity and irreducibility), and a mild restriction on the level of the n-dimensional representation.