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arXiv · 2403.01963

Hurwitz numbers for reflection groups $G(m,1,n)$

Raphaël Fesler·Denis Gorodkov·Maksim Karev
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Abstract

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 $\tau$-function of the KP hierarchy. Finally we provide an ELSV-formula type for these new Hurwitz numbers.

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Raphaël Fesler, Denis Gorodkov, Maksim Karev. 2024-03-04. Hurwitz numbers for reflection groups $G(m,1,n)$. https://arxiv.org/abs/2403.01963

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