Wreath Hurwitz numbers,colored cut-and-join equations,and 2-Toda hierarchy

作     者：ZHANG HanXiong ZHOU Jian 

作者机构：Department of Mathematical Sciences Tsinghua University Beijing 100084 China Email: zhanghanxiong @163. corn jzhou~math tsinghua edu. cn 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2012年第55卷第8期

页      面：1627-1646页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10425101,10631050) National Basic Research Program of China(973Project)(Grant No.2006cB805905) 

主　　题：Hurwitz number wreath product cut-and-join equation integrable hierarchy 

摘      要：Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz *** prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand-join ***,H G·(t;p +,p) is a product of several copies of tau functions of the 2-Toda hierarchy,in independent *** generalize the corresponding results for ordinary Hurwitz numbers.