Let F F be a finite group and X X be a complex quasi-projective F F -variety. For r ∈ N r\in {\mathbb{N}} , we consider the mixed Hodge-Deligne polynomials of quotients X r / F {X}^{r}\hspace{-0.15em}\text{/}\hspace{-0.08em}F , where F F acts diagonally, and compute them for certain classes of varieties X X with simple mixed Hodge structures (MHSs). A particularly interesting case is when X X is the maximal torus of an affine reductive group G G , and F F is its Weyl group. As an application, we obtain explicit formulas for the Hodge-Deligne and E E -polynomials of (the distinguished component of) G G -character varieties of free abelian groups. In the cases G = G L ( n , C ) G=GL\left(n,{\mathbb{C}}\hspace{-0.1em}) and S L ( n , C ) SL\left(n,{\mathbb{C}}\hspace{-0.1em}) , we get even more concrete expressions for these polynomials, using the combinatorics of partitions.

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