Cheng Shu:Mixed Hodge polynomial of character variety

Abstract: Hausel, Letellier and Rodriguez-Villegas computed the E-polynomial of character varieties with generic semi-simple conjugacy classes. Their computation led to a conjectural formula for the mixed Hodge polynomial of character varieties. We will recall their results and introduce a new family of character varieties that are unitary in the global sense. The same method gives a conjectural formula for the mixed Hodge polynomial, which is built of Macdonald polynomials and wreath Macdonald polynomials.