$\mathfrak{b}$-Hurwitz numbers from refined topological recursion
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917342853726208 |
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| author | Chidambaram, Nitin Kumar Dołęga, Maciej Osuga, Kento |
| author_facet | Chidambaram, Nitin Kumar Dołęga, Maciej Osuga, Kento |
| contents | We prove that single $G$-weighted $\mathfrak{b}$-Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights $G$. Consequently, the $\mathfrak{b}$-Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of $\mathfrak{b}$-monotone Hurwitz numbers, and the enumeration of maps and bipartite maps (with internal faces) on non-oriented surfaces. As an application, we prove that the correlators of the Gaussian, Jacobi and Laguerre $β$-ensembles are computed by refined topological recursion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathfrak{b}$-Hurwitz numbers from refined topological recursion Chidambaram, Nitin Kumar Dołęga, Maciej Osuga, Kento Combinatorics Mathematical Physics Algebraic Geometry Representation Theory We prove that single $G$-weighted $\mathfrak{b}$-Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights $G$. Consequently, the $\mathfrak{b}$-Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of $\mathfrak{b}$-monotone Hurwitz numbers, and the enumeration of maps and bipartite maps (with internal faces) on non-oriented surfaces. As an application, we prove that the correlators of the Gaussian, Jacobi and Laguerre $β$-ensembles are computed by refined topological recursion. |
| title | $\mathfrak{b}$-Hurwitz numbers from refined topological recursion |
| topic | Combinatorics Mathematical Physics Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2412.17502 |