Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations

Let $X$ be a smooth, separated, geometrically connected scheme defined over a number field $K$ and $\{{\rho }_{\lambda }{\}}_{\lambda }$ a system of n-dimensional semisimple $\lambda$-adic representations of the étale fundamental group of $X$ such that for each closed point $x$ of $X$, the specialization $\{{\rho }_{\lambda ,x}{\}}_{\lambda }$ is a compatible system of Galois representations under mild local conditions. For almost all $\lambda$, we prove that any type A irreducible subrepresentation of ${\rho }_{\lambda }\otimes {\bar{\mathbb{Q}}}_{\mathrm{\ell }}$ is residually irreducible. When $K$ is totally real or CM, $n\le 6$, and $\{{\rho }_{\lambda }{\}}_{\lambda }$ is the compatible system of Galois representations of $K$ attached to a regular algebraic, polarized, cuspidal automorphic representation of ${\mathrm{G}\mathrm{L}}_n({\mathbb{A}}_K)$, for almost all $\lambda$ we prove that ${\rho }_{\lambda }\otimes {\bar{\mathbb{Q}}}_{\mathrm{\ell }}$ is (i) irreducible and (ii) residually irreducible if in addition $K=\mathbb{Q}$.