Arithmetic and representation theory of wild character varieties

  • Tamás Hausel

    Institute of Science and Technology Austria, Klosterneuburg, Austria
  • Martin Mereb

    Universidad de Buenos Aires, Argentina
  • Michael Lennox Wong

    Universität Duisburg-Essen, Germany
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Abstract

We count points over a finite field on wild character varieties of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras. Our result leads to the conjecture that the mixed Hodge polynomials of these character varieties agree with the previously conjectured perverse Hodge polynomials of certain twisted parabolic Higgs moduli spaces, indicating the possibility of a conjecture for a suitable wild Hitchin system.

Cite this article

Tamás Hausel, Martin Mereb, Michael Lennox Wong, Arithmetic and representation theory of wild character varieties. J. Eur. Math. Soc. 21 (2019), no. 10, pp. 2995–3052

DOI 10.4171/JEMS/896