This paper realizes of two families of combinatorial symmetric functions via the complex character theory of the finite general linear group $\mathrm{ GL}_{ n}(\mathbb{ F}_{ q})$: chromatic quasisymmetric functions and vertical strip LLT polynomials. The associated $\mathrm{ GL}_{ n}(\mathbb{ F}_{ q})$ characters are elementary in nature and can be obtained by induction from certain well-behaved characters of the unipotent upper triangular groups $\mathrm{ UT}_{ n}(\mathbb{ F}_{ q})$. The proof of these results also gives a general Hopf algebraic approach to computing the induction map. Additional results include a connection between the relevant $\mathrm{ GL}_{ n}(\mathbb{ F}_{ q})$ characters and Hessenberg varieties and a re-interpretation of known theorems and conjectures about the relevant symmetric functions in terms of $\mathrm{ GL}_{ n}(\mathbb{ F}_{ q})$.
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