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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 421, Pages 33–46 (Mi znsl5747)  
This article is cited in 2 scientific papers (total in 2 papers)

A combinatorial interpretation of the scalar products of state vectors of integrable models

N. M. Bogoliubov, C. Malyshev

St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
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Abstract: The representation of Bethe wave functions of certain integrable models via Schur functions allows one to apply the well-developed theory of symmetric functions to the calculation of thermal correlation functions. The algebraic relations arising in the calculation of scalar products and correlation functions are based on the Binet–Cauchy formula for the Schur functions. We provide a combinatorial interpretation of the formula for the scalar products of Bethe state vectors in terms of nests of self-avoiding lattice paths constituting so-called watermelon configurations. The proposed interpretation is, in turn, related to the enumeration of boxed plane partitions.
Key words and phrases: Schur functions, self-avoiding lattice paths, boxed plane partitions.
Received: 28.11.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 200, Issue 6, Pages 662–670
DOI: https://doi.org/10.1007/s10958-014-1956-2
Bibliographic databases:
Document Type: Article
UDC: 519.248.25
Language: English
Citation: N. M. Bogoliubov, C. Malyshev, “A combinatorial interpretation of the scalar products of state vectors of integrable models”, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Zap. Nauchn. Sem. POMI, 421, POMI, St. Petersburg, 2014, 33–46; J. Math. Sci. (N. Y.), 200:6 (2014), 662–670
Citation in format AMSBIB
\Bibitem{BogMal14}
\by N.~M.~Bogoliubov, C.~Malyshev
\paper A combinatorial interpretation of the scalar products of state vectors of integrable models
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIII
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 421
\pages 33--46
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5747}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 200
\issue 6
\pages 662--670
\crossref{https://doi.org/10.1007/s10958-014-1956-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84940258802}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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