Hurwitz numbers for reflection groups
Raphaël Fesler, Denis Gorodkov, Maksim Karev
Source abstract
We build a parallel theory of simple Hurwitz numbers for the reflection groups G(m,1,n) . We study analogs of the cut-and-join operators. An algebraic description as well as a description of Hurwitz numbers in terms of ramified coverings is provided. An explicit formula for them in terms of Schur polynomials is given. In addition, the generating function of G(m,1,n) -Hurwitz numbers is shown to give rise to an m independent-variables \tau -function of the KP hierarchy. Finally, we provide an ELSV-type formula for these new Hurwitz numbers. These results extend the results of Fesler (2023).
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