On the images of certain $G_2$-valued automorphic Galois representations

Adrian Zenteno

In this paper we study the images of certain families $\{{\rho }_{\pi ,\ell }{\}}_{\ell }$ of $G_2$-valued Galois representations of $\mbox{Gal}(\overline{F}/F)$ associated to $L$-algebraic regu…