Hurwitz numbers for reflection groups G (m, 1, n)

We are extending results from B-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 -function of the KP hierarchy. Finally we provide an ELSV-formula type for these new Hurwitz numbers.