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](https://en.wikipedia.org/wiki/Riemann%E2%80%93Hilbert_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](https://arxiv.org/pdf/1711.04148.pdf)). 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 $n\geq 2$, 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?



Representation theory of higher homotopy groups
There are many results that generalize the Riemann–Hilbert correspondence from the fundamental groupoid to the fundamental ∞-groupoid, for example:


* Jonathan Block, Aaron Smith. [A Riemann–Hilbert correspondence for infinity local systems](https://arxiv.org/abs/0908.2843).
* Joseph Chuang, Julian Holstein, Andrey Lazarev. [Maurer-Cartan moduli and theorems of Riemann-Hilbert type](https://arxiv.org/abs/1802.02549).
* Manuel Rivera, Mahmoud Zeinalian. [The colimit of an ∞-local system as a twisted tensor product](https://arxiv.org/abs/1805.01264).
* Camilo Arias Abad, Florian Schaetz. [Flat Z-graded connections and loop spaces](https://arxiv.org/abs/1510.04975).
* Julian V. S. Holstein. [Morita cohomology](https://arxiv.org/abs/1404.1327).
* Camilo Arias Abad, Florian Schaetz. [The A\_infty de Rham theorem and integration of representations up to homotopy](https://arxiv.org/abs/1011.4693).
* Vincent Braunack-Mayer. [Strict algebraic models for rational parametrised spectra II](https://arxiv.org/abs/2011.06307).
* Camilo Arias Abad, Sebastian Velez Vasquez. [The higher Riemann-Hilbert correspondence and principal 2-bundles](https://arxiv.org/abs/2007.07941).


For the higher Galois theory, see


* Marc Hoyois. [Higher Galois theory](https://arxiv.org/abs/1506.07155).


