2023/02/11 by Fesler, Raphaël
#57N05 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2302.05664
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.