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Zap. Nauchn. Sem. POMI, 2010, Volume 378, Pages 111–132 (Mi znsl3831)  

This article is cited in 1 scientific paper (total in 1 paper)

Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case

N. V. Tsilevich

St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia

Abstract: This paper is a part of the project suggested by A. M. Vershik and the author and aimed to combine the known results on the representation theory of finite and infinite symmetric groups and a circle of results related to the quantum inverse scattering method and Bethe ansatz. In this first part, we consider the simplest spectral properties of a distinguished operator in the group algebra of the symmetric group, which we call the periodic Coxeter Laplacian. Namely, we study this operator in the two-row representations of symmetric groups and in the “ferromagnetic” asymptotic mode. Bibl. 11 titles.

Key words and phrases: Coxeter Laplacian, representations of symmetric groups, Bethe ansatz.

Full text: PDF file (637 kB)
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English version:
Journal of Mathematical Sciences (New York), 2011, 174:1, 58–70

UDC: 517.98+517.958
Received: 12.09.2010
Language:

Citation: N. V. Tsilevich, “Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case”, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Zap. Nauchn. Sem. POMI, 378, POMI, St. Petersburg, 2010, 111–132; J. Math. Sci. (N. Y.), 174:1 (2011), 58–70

Citation in format AMSBIB
\Bibitem{Tsi10}
\by N.~V.~Tsilevich
\paper Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 378
\pages 111--132
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3831}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 174
\issue 1
\pages 58--70
\crossref{https://doi.org/10.1007/s10958-011-0281-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952817119}


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    This publication is cited in the following articles:
    1. J. Math. Sci. (N. Y.), 181:6 (2012), 914–920  mathnet  crossref
  • Записки научных семинаров ПОМИ
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