Irreducibility of automorphic Galois representations of low dimensions

Abstract

Let $$\pi $$ be a polarizable, regular algebraic, cuspidal automorphic representation of $$\text { GL }_n(\mathbb {A}_F)$$ , where F is an imaginary CM field and $$n \le 6$$ . We show that there is a Dirichlet density 1 set $$\mathfrak {L}$$ of rational primes, such that for all $$l\in \mathfrak {L}$$ , the l-adic Galois representations associated to $$\pi $$ are irreducible.