FlorentinoSilva, Jaime2021-06-142021-06-142021-05-21FLORENTINO, Carlos; SILVA, Jaime – Hodge-deligne polynomials of character varieties of free abelian groups. Open Mathematics. ISSN 2391-5455. Vol. 19, N.º 1 (2021), pp. 338-362.2391-5455http://hdl.handle.net/10400.21/13443Let F be a finite group and X be a complex quasi-projective F-variety. For r is an element of N, we consider the mixed Hodge-Deligne polynomials of quotients X-r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple mixed Hodge structures (MHSs). A particularly interesting case is when X is the maximal torus of an affine reductive group G, and F is its Weyl group. As an application, we obtain explicit formulas for the Hodge-Deligne and E-polynomials of (the distinguished component of) G-character varieties of free abelian groups. In the cases G = GL(n, C) and SL(n, C), we get even more concrete expressions for these polynomials, using the combinatorics of partitions.engFree abelian groupCharacter varietyMixed Hodge structuresHodge-Deligne polynomialsEquivariant E-polynomialsFinite quotientsjournal article10.1515/math-2021-0038