Plethystic identities and mixed Hodge structures of character varieties
  I demonstrate how certain identities for Macdonald's polynomials established by Garsia, Haiman and Tesler, together with the conjecture of Hausel, Letellier and Villegas imply explicit relations between mixed Hodge polynomials of different character varieties. 
Anton Mellit
math.AG math.CO math.RT