Counting points on generic character varieties

2024/09/07 by Masoud Kamgarpour, GyeongHyeon Nam, Kamgarpour, Masoud +5 · 1 citation
Computer Science · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #Constraint Satisfaction and Optimization #FOS: Mathematics #Polynomial and algebraic computation #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2409.04735

openalex publication_date 2024/09/07 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

We count points on character varieties associated with punctured surfaces and regular semisimple generic conjugacy classes in reductive groups. We find that the number of points are palindromic polynomials. This suggests a P=W conjecture for these varieties. We also count points on the corresponding additive character varieties and find that the number of points are also polynomials, which we conjecture have non-negative coefficients. These polynomials can be considered as the reductive analogues of the Kac polynomials of comet-shaped quivers.

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• Deformation theory of parabolic representation pairs

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