Hurwitz numbers for reflection groups $G(m,1,n)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910353152016384 |
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| author | Fesler, Raphaël Gorodkov, Denis Karev, Maksim |
| author_facet | Fesler, Raphaël Gorodkov, Denis Karev, Maksim |
| contents | We are extending results from \cite{B-Hurwitz} by building a parallel theory of simple Hurwitz numbers for the reflection groups $G(m,1,n)$. We also study analogs of the cut-and-join operators. An algebraic description as well as a description in terms of ramified covering of Hurwitz numbers is provided. An explicit formula for them in terms of Schur polynomials are provided. In addition the generating function of $G(m,1,n)$-Hurwitz numbers is shown to give rise to $m$ independent variables $τ$-function of the KP hierarchy. Finally we provide an ELSV-formula type for these new Hurwitz numbers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_01963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hurwitz numbers for reflection groups $G(m,1,n)$ Fesler, Raphaël Gorodkov, Denis Karev, Maksim Combinatorics Algebraic Geometry 05A15, 14N10 We are extending results from \cite{B-Hurwitz} by building a parallel theory of simple Hurwitz numbers for the reflection groups $G(m,1,n)$. We also study analogs of the cut-and-join operators. An algebraic description as well as a description in terms of ramified covering of Hurwitz numbers is provided. An explicit formula for them in terms of Schur polynomials are provided. In addition the generating function of $G(m,1,n)$-Hurwitz numbers is shown to give rise to $m$ independent variables $τ$-function of the KP hierarchy. Finally we provide an ELSV-formula type for these new Hurwitz numbers. |
| title | Hurwitz numbers for reflection groups $G(m,1,n)$ |
| topic | Combinatorics Algebraic Geometry 05A15, 14N10 |
| url | https://arxiv.org/abs/2403.01963 |