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

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.

72 pages. At the suggestion of the anonymous referee, we expanded Sections 3 and 4 of the paper, and improved the exposition at several points