Generating series for the $E$-polynomials of $GL(n,\mathbb{C})$-character varieties

With G=GL(n,C), let ${\mathcal{X}}_{\mathrm{\Gamma }}G$ be the G-character variety of a given finitely presented group $\mathrm{\Gamma }$, and let $$\mathcal{X}$^{irr}{\Gamma}G \subset $\mathcal{X}${\Gamma}G$ be the locus of irreducible representation conjugacy classes. We provide a concrete relation, in terms of plethystic functions, between the generating series for E- polynomials of ${\mathcal{X}}_{\mathrm{\Gamma }}G$ and the one for ${\mathcal{X}}_{\mathrm{\Gamma }}^{irr}G$, generalizing a formula of Mozgovoy-Reineke [MR]. The proof uses a natural stratification of ${\mathcal{X}}_{\mathrm{\Gamma }}G$ coming from affine GIT, the combinatorics of partitions, and the formula of MacDonald-Cheah for symmetric products; we also adapt it to the so-called Cartan brane in the moduli space of Higgs bundles. Combining our methods with arithmetic ones yields explicit expressions for the E-polynomials of the irreducible stratum of GL(n,C)-character varieties of some groups $\mathrm{\Gamma }$, including surface groups, free groups, and torus knot groups, for low values of $n$.