Counting points on generic character varieties
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911390604722176 |
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| author | Kamgarpour, Masoud Nam, GyeongHyeon Whitbread, Bailey Giannini, Stefano |
| author_facet | Kamgarpour, Masoud Nam, GyeongHyeon Whitbread, Bailey Giannini, Stefano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting points on generic character varieties Kamgarpour, Masoud Nam, GyeongHyeon Whitbread, Bailey Giannini, Stefano Algebraic Geometry Representation Theory 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. |
| title | Counting points on generic character varieties |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2409.04735 |