  Given a finitely-generated group $\pi$ and a linear algebraic group $G$, the
representation variety Hom$(\pi,G)$ has a natural filtration by the
characteristic varieties associated to a rational representation of $G$. Its
algebraic counterpart, the space of $\mathfrak{g}$-valued flat connections on a
commutative, differential graded algebra $(A,d)$ admits a filtration by the
resonance varieties associated to a representation of $\mathfrak{g}$. We
establish here a number of results concerning the structure and qualitative
properties of these embedded resonance varieties, with particular attention to
the case when the rank 1 resonance variety decomposes as a finite union of
linear subspaces. The general theory is illustrated in detail in the case when
$\pi$ is either an Artin group, or the fundamental group of a smooth,
quasi-projective variety.
