Papers › Counting points on generic character varieties
Counting points on generic character varieties
Masoud Kamgarpour, GyeongHyeon Nam, Bailey Whitbread, Stefano Giannini
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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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