On the E-polynomials of a family of character varieties
MetadataShow full item record
We compute the E-polynomials of a family of twisted character varieties M [superscript g] (Sl [subscript n]) by proving they have polynomial count, and applying a result of N. Katz on the counting functions. To compute the number of F [subscript q]-points of these varieties as a function of q, we used a formula of Frobenius. Our calculations made use of the character tables of Gl [subscript n](q) and Sl subscript n](q), previously computed by J. A. Green and G. Lehrer, and a result of Hanlon on the Möbius function of a subposet of set-partitions. The Euler Characteristics of the M [superscript g] (Sl [subscript n]) are calculated then with these polynomial.