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arXiv · 2302.05664

Hurwitz numbers for reflection groups $B$ and $D$

Raphaël Fesler
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Abstract

We are building a theory of simple Hurwitz numbers for the reflection groups B and D parallel to the classical theory for the symmetric group. We also study analogs of the cut-and-join operators. An algebraic description of Hurwitz numbers and an explicit formula for them in terms of Schur polynomials are provided. We also relate Hurwitz numbers for B and D to ribbon decomposition of surfaces with boundary -- a similar result for the symmetric group was proved earlier by Yu.Burman and the author. Finally, the generating function of B-Hurwitz numbers is shown to give rise to two independent tau-function of the KP hierarchy.

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Raphaël Fesler. 2023-02-11. Hurwitz numbers for reflection groups $B$ and $D$. https://arxiv.org/abs/2302.05664

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