On irreducibility of certain low dimensional automorphic Galois representations

2025/10/14 by Dai, Boyi
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.12496

Abstract

We study irreducibility of Galois representations ρ_π,λ associated to a n=7 or 8-dimensional regular algebraic essentially self-dual cuspidal automorphic representation π of GL_n(\mathbbA_ℚ). We show ρ_π,λ is irreducible for all but finitely many λ under the following extra conditions. (i) If n=7, and there exists no λ such that the Lie type of ρ_π,λ is the standard representation of exceptional group G₂. (ii) If n=8, and when there exist infinitely many λ such that the Lie type of ρ_π,λ is the spin representation of SO₇, we assume there exist no three distinct Hodge-Tate weights form a 3-term arithmetic progression.

Citations

• Irreducibility of polarized automorphic Galois representations in infinitely many dimensions
• Monodromy and irreducibility of type A₁ automorphic Galois representations
• Five-dimensional compatible systems and the Tate conjecture for elliptic surfaces
• Weak abelian direct summands and irreducibility of Galois representations
• Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations
• On the sign of regular algebraic polarizable automorphic representations
• Monodromy of Galois representations and equal-rank subalgebra equivalence
• Irreducibility of automorphic Galois representations of GL(n), n at most\n 5
• Potential automorphy and change of weight

Related

• Irreducibility of automorphic Galois representations of GL(n), n at most\n 5
• On the images of certain G₂-valued automorphic Galois representations
• Irreducibility of polarized automorphic Galois representations in infinitely many dimensions
• On The Image of Automorphic Galois Representations
• Irreducibility and cuspidality