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Description
The geometry of the moduli spaces appearing in the non-abelian Hodge theory of a Riemann surface (i.e. moduli spaces of Higgs bundles and character stacks) is well understood in the smooth case. In the singular case, the situation is more complicated. In this article, we give a conjectural formula for the mixed Poincaré series of character stacks for Riemann surfaces. Furthermore, we verify it under Euler's specialization (i.e., we calculate the E-series). Such a formula was previously known only in the smooth case, thanks to the work of Hausel, Letellier, and Rodriguez-Villegas. Our formula expresses the singular case as a sort of "symmetric power" of the smooth ones. Similar results have appeared in multiple works in related areas. The results of the article provide important evidence in support of the chi-independence property of the coomology of these stacks.
