Counting stringy points on a family of character varieties
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913574419431424 |
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| author | de Amorin, Lucas Mereb, Martin |
| author_facet | de Amorin, Lucas Mereb, Martin |
| contents | We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. This leads to formulas for their stringy E-polynomials. In particular, they satisfy the Betti Topological Mirror Symmetry Conjecture of T. Hausel and M. Thaddeus, as well as a refinement regarding isotypic components. Our proof is based on a Frobenius' type formula for Clifford's type settings and an analysis of it in a specific set-up related to regular wreath products with cyclic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting stringy points on a family of character varieties de Amorin, Lucas Mereb, Martin Algebraic Geometry Representation Theory We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. This leads to formulas for their stringy E-polynomials. In particular, they satisfy the Betti Topological Mirror Symmetry Conjecture of T. Hausel and M. Thaddeus, as well as a refinement regarding isotypic components. Our proof is based on a Frobenius' type formula for Clifford's type settings and an analysis of it in a specific set-up related to regular wreath products with cyclic groups. |
| title | Counting stringy points on a family of character varieties |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2411.05563 |