Journal
RUSSIAN MATHEMATICAL SURVEYS
Volume 70, Issue 3, Pages 453-482Publisher
TURPION LTD
DOI: 10.1070/RM2015v070n03ABEH004952
Keywords
integrable systems; Kadomtsev-Petviashvili hierarchy; Toda lattice hierarchy; boson-fermion correspondence; Hurwitz numbers
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Funding
- Russian Foundation for Basic Research [13-01-00383-a]
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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.
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