Hurwitz numbers for reflection groups $G(m,1,n)$
Combinatorics
2024-03-05 v1 Algebraic Geometry
Abstract
We are extending results from \cite{B-Hurwitz} by building a parallel theory of simple Hurwitz numbers for the reflection groups . 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 -Hurwitz numbers is shown to give rise to independent variables -function of the KP hierarchy. Finally we provide an ELSV-formula type for these new Hurwitz numbers.
Keywords
Cite
@article{arxiv.2403.01963,
title = {Hurwitz numbers for reflection groups $G(m,1,n)$},
author = {Raphaël Fesler and Denis Gorodkov and Maksim Karev},
journal= {arXiv preprint arXiv:2403.01963},
year = {2024}
}