Hopf algebras are a nice way to incorporate algebraic tools into the study of combinatorial objects with recursive structure, and in some cases these combinatorial Hopf structures also encode representation theoretic information. This talk will use a new example of this phenomenon to expand on this general idea. On the combinatorial side is the chromatic quasisymmetric function, a q-analogue of Stanley’s chromatic symmetric function of a graph; this function can be realized as the image of a homomorphism between Hopf algebra structures on graphs and (quasi-)symmetric functions. On the representation theory side is a collection of GLn(Fq)-modules that arise in the study of the maximal unipotent upper triangular subgroup of GLn(Fq). I will show that the GLn(Fq)-modules are, up to a canonical equivalence, the image of the same homomorphism mentioned above; thus each module is a representation-theoretic realization of some chromatic quasisymmetric function. Along the way I will define a new Hopf algebra of class functions on the unipotent upper triangular groups and use lots of pictures and examples.