On the Image of Automorphic Galois Representations
Abstract
Abstract In this paper, we study extra-twists for automorphic representations of ${\textrm{GL}}_{n}$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic representations of ${\textrm{GL}}_{3}$ over totally real fields. We also formulate a conjecture for the ${\textrm{GL}}_{n}$-case, inspired by 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.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Polynomial and algebraic computation
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 8
- Publication date
- 30 March 2026
- Language
- EN