Integrality of Hausel–Letellier–Villegas kernels


We prove that the coefficients of the generating function of Hausel, Letellier, and Rodriguez-Villegas and its recent generalization by Carlsson and Rodriguez-Villegas, which according to various conjectures should compute mixed Hodge numbers of character varieties and moduli spaces of Higgs bundles of curves of genus $g$ with $n$ punctures, are polynomials in $q$ and $t$ with integer coefficients for any $g,n\geq 0$.

Duke Math. J. 167 (2018), no. 17, 3171–3205