On the E-polynomials of a family of Character Varieties

2010/06/07 by Martı́n Mereb, Mereb, Martin · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1006.1286

openalex publication_date 2010/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• The Self-Duality Equations on a Riemann Surface
• Algebraic Groups Over Finite Fields

Cited by

• Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus
• Intersection cohomology of rank two character varieties of surface\n groups

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