Year: 2023
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Fesler, Raphaël
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4320838879