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arXiv · 2409.04735

Counting points on generic character varieties

Masoud Kamgarpour·GyeongHyeon Nam·Bailey Whitbread·Stefano Giannini
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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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Masoud Kamgarpour, GyeongHyeon Nam, Bailey Whitbread, Stefano Giannini. 2024-09-07. Counting points on generic character varieties. https://arxiv.org/abs/2409.04735

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