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Russian Mathematical Surveys, 2015, Volume 70, Issue 3, Pages 453–482
DOI: https://doi.org/10.1070/RM2015v070n03ABEH004952 (Mi rm9661) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Combinatorial solutions to integrable hierarchies

M. È. Kazarianab, S. K. Landob

a Steklov Mathematical Institute of Russian Academy of Sciences
b National Research University Higher School of Economics
English version PDF (605 kB) Citations (26) Russian version article
References:
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DOI: https://doi.org/10.1070/RM2015v070n03ABEH004952
Abstract: 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.
Bibliography: 34 titles.
Keywords: integrable systems, Kadomtsev–Petviashvili hierarchy, Toda lattice hierarchy, boson-fermion correspondence, Hurwitz numbers.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00383-а
Received: 25.12.2014
Bibliographic databases:
Document Type: Article
UDC: 512.542.74+515.162.2+517.958:530.145
MSC: Primary 14H70, 37K20, 81R12; Secondary 57R56
Language: English
Original paper language: Russian
Citation: M. È. Kazarian, S. K. Lando, “Combinatorial solutions to integrable hierarchies”, Russian Math. Surveys, 70:3 (2015), 453–482
Citation in format AMSBIB
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\by M.~\`E.~Kazarian, S.~K.~Lando
\paper Combinatorial solutions to integrable hierarchies
\jour Russian Math. Surveys
\yr 2015
\vol 70
\issue 3
\pages 453--482
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    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:1400
    Russian version PDF:562
    English version PDF:53
    References:76
    First page:82
     
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