Combinatorial solutions to integrable hierarchies

被引：26

作者：

Kazarian, M. E. ^{[1
,2
]}

Lando, S. K. ^{[2
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Moscow 117901, Russia

[2] Natl Res Univ, Higher Sch Econ, Moscow, Russia

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2015年 / 70卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

integrable systems; Kadomtsev-Petviashvili hierarchy; Toda lattice hierarchy; boson-fermion correspondence; Hurwitz numbers; HURWITZ NUMBERS; TODA EQUATIONS;

D O I：

10.1070/RM2015v070n03ABEH004952

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper reviews modern approaches to the construction of formal solutions to integrable hierarchies of mathematical physics whose coefficients are answers to various enumerative problems. The relationship between these approaches and the combinatorics of symmetric groups and their representations is explained. Applications of the results to the construction of efficient computations in problems related to models of quantum field theories are described.

引用

页码：453 / 482

页数：30

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