Wreath Hurwitz numbers, colored cut-and-join equations, and 2-Toda hierarchy
type: Item
instance of: scholarly article
title: Wreath Hurwitz numbers, colored cut-and-join equations, and 2-Toda hierarchy
zbMATH Open document ID: 1298.14034
author: HanXiong Zhang
author: Jian Zhou
published in: Science China. Mathematics
publication date: 2013-01-28T00:00:00Z
review text: For an arbitrary finite group \(G\), it is proved that the generating function of \(G\)-wreath double Hurwitz numbers satisfies a differential equation and that this generating function is a product of several copies of tau-functions of the \(2\)-Toda hierarchy, in independent variables.
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 6131109
zbMATH Keywords: Riemann surface
zbMATH Keywords: generating function
zbMATH Keywords: symmetric group
zbMATH Keywords: Hurwitz number
zbMATH Keywords: wreath product
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: s11425-012-4383-1
OpenAlex ID: W1998307763
cites work: Gromov-Witten theory of Deligne-Mumford stacks
cites work: Topological strings and integrable hierarchies
cites work: The topological vertex
cites work: A matrix model for simple Hurwitz numbers, and topological recursion
cites work: Q4409407
cites work: Localization, Hurwitz numbers and the Witten conjecture
cites work: Q4858408
cites work: On Hurwitz numbers and Hodge integrals
cites work: Virasoro algebra and wreath product convolution
cites work: Transitive factorisations into transpositions and holomorphic mappings on the sphere
cites work: The number of ramified coverings of the sphere by the torus and surfaces of higher genera
cites work: A short proof of the λg -conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
cites work: Abelian Hurwitz-Hodge integrals
cites work: Intersection theory on the moduli space of curves and the matrix Airy function
cites work: A mathematical theory of the topological vertex
cites work: A proof of a conjecture of Mariño-Vafa on Hodge integrals
cites work: A formula of two-partition Hodge integrals
cites work: Q4328336
cites work: Q4409413
cites work: Toda equations for Hurwitz numbers
cites work: Infinite wedge and random partitions
cites work: Q3697941
cites work: Q4012873
cites work: Hodge integrals and integrable hierarchies
DOI: 10.1007/S11425-012-4383-1
description: scientific article; zbMATH DE number 6131109