English

On The Image of Automorphic Galois Representations

Number Theory 2025-02-18 v1

Abstract

In this paper, we study extra-twists for automorphic representations of GLn\mathrm{GL}_n and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic representations of GL3\mathrm{GL}_3 over totally real fields. We also formulate a conjecture for the GLn\mathrm{GL}_n-case and show how it follows from some standard conjectures in the Langlands program. Finally, assuming the existence of a motive associated with the representation, we study the relation of our constructions with the Mumford-Tate group.

Keywords

Cite

@article{arxiv.2502.10799,
  title  = {On The Image of Automorphic Galois Representations},
  author = {Alireza Shavali},
  journal= {arXiv preprint arXiv:2502.10799},
  year   = {2025}
}