Duke Mathematical Journal

Integrality of Hausel–Letellier–Villegas kernels

Anton Mellit

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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,n0.

Article information

Duke Math. J., Volume 167, Number 17 (2018), 3171-3205.

Received: 27 October 2016
Revised: 10 May 2018
First available in Project Euclid: 10 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05]
Secondary: 05E05: Symmetric functions and generalizations

character varieties Higgs bundles generating functions Hodge polynomials Macdonald polynomials


Mellit, Anton. Integrality of Hausel–Letellier–Villegas kernels. Duke Math. J. 167 (2018), no. 17, 3171--3205. doi:10.1215/00127094-2018-0030. https://projecteuclid.org/euclid.dmj/1539137165

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