field $F$ came (in some precise sense) from an automorphic representation for ${\operatorname{GL}}_n/F$, and then analytically continuing the $L$-function of this automorphic representation instead.

One might ask whether one can associate “Galois representations” to automorphic representations for an arbitrary connected reductive group over a number field. There are several approaches to formalising this problem. Firstly one could insist on working with all automorphic representations and attempt to associate to them complex representations of a “Langlands group”, a group whose existence is only conjectural but which, if it exists, should be much bigger than the absolute Galois group of the number field (and even much bigger than the Weil group of the number field)—a nice reference for a rigorous formulation of a conjecture here is [@arthur:note]. Alternatively one could restrict to automorphic representations that are “algebraic” in some reasonable sense, and in this case one might attempt to associate certain complex representations of the fundamental group of some Tannakian category of motives, a group which might either be a pro-algebraic group scheme or a topological group. Finally, following the original examples of Weil and Deligne, one might again restrict to algebraic automorphic representations, and then attempt to associate compatible systems of 