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Zap. Nauchn. Sem. 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

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.

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English version:
Journal of Mathematical Sciences (New York), 2014, 200:6, 662–670

UDC: 519.248.25
Received: 28.11.2013
Language:

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. J. Math. Sci. (N. Y.), 216:1 (2016), 8–22  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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