摘要
Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz numbers.We prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand-join equation.Furthermore,H G·(t;p +,p) is a product of several copies of tau functions of the 2-Toda hierarchy,in independent variables.These generalize the corresponding results for ordinary Hurwitz numbers.
Let G be arbitrary finite group, define H·G（t;p＋,p ） to be the generating function of G-wreath double Hurwitz numbers. We prove that H·G（t; p＋,p-） satisfies a differential equation called the colored cut- and-join equation. Furthermore, H·G（t;p＋,p-） is a product of several copies of tau functions of the 2-Toda hierarchy, in independent variables. These generalize the corresponding results for ordinary Hurwitz numbers.
基金
supported by National Natural Science Foundation of China(Grant Nos.10425101,10631050)
National Basic Research Program of China(973Project)(Grant No.2006cB805905)
