I’ve seen some works on the representation of fundamental groups, which are (at least for me) quite important topic in mathematics. For example, Riemann-Hilbert correspondence relates representation of a fundamental group of complex algebraic variety with differential equations on it. (There’s also a result in positive characteristic by Bhatt-Lurie). Also, etale fundamental group and its representation is also important in number theory because it is closely related to Galois groups. (I don’t know much about this though). However, I can’t find any works that studies about representation of higher homotopy groups $pi_{n}$ (or etale homotopy groups, whatever it is). Although $pi_n$ is abelian for $ngeq 2$, there might exist some nontrivial stuff that $pi_n$ can act naturally so that we can study about its representations (which would be 1-dimensional if irreducible, though). Could you give any examples if there’s any interesting works about such things?