2024/03/04 by Raphaël Fesler, Fesler, Raphaël, Denis Gorodkov +3
Computer Science · Mathematics · #05A15 #14N10 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2403.01963
openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are extending results from \citeB-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.