English

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

Number Theory 2025-09-18 v4

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.

Keywords

Cite

@article{arxiv.1611.06918,
  title  = {Automorphy of $\mathrm{GL}_2\otimes \mathrm{GL}_n$ in the self-dual case},
  author = {Sara Arias-de-Reyna and Luis Dieulefait and Josu Pérez},
  journal= {arXiv preprint arXiv:1611.06918},
  year   = {2025}
}

Comments

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