On the E-polynomials of a family of Character Varieties

Abstract

We compute the E-polynomials of a family of twisted character varieties by proving they have polynomial count, and applying a result of N. Katz on the counting functions. To compute the number of GF(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(n,q) and Sl(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 these character varieties are calculated with these polynomial.

References in corpus (3)

• Mirror symmetry, Langlands duality, and the Hitchin system
• Topological Reduction of 4D SYM to 2D $\sigma$--Models
• Chern-Simons Theory with Finite Gauge Group

Cited by in corpus (15)

• Global topology of the Hitchin system
• Arithmetic of singular character varieties and their $E$-polynomials
• Virtual classes of parabolic ${\mathrm{SL}}_2(\mathbb{C})$-character varieties
• Hodge-Deligne polynomials of character varieties of abelian groups
• Topology of Hitchin systems and Hodge theory of character varieties: the case A_1
• On the P=W conjecture for ${\mathrm{SL}}_n$
• Motivic theory of representation varieties via Topological Quantum Field Theories
• Intersection cohomology of rank two character varieties of surface groups
• E-polynomials of $PGL(2,\mathbb{C})$-character varieties of surface groups
• Representation variety for the rank one affine group
• E-polynomials of the SL(2,C)-character varieties of surface groups
• Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories
• Pseudo-quotients of algebraic actions and their application to character varieties
• Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus
• The point counting problem in representation varieties of torus knots