Geodesic
Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 111-132

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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. 
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     author = {N. V. Tsilevich},
     title = {Spectral properties of the periodic {Coxeter} {Laplacian} in the two-row ferromagnetic case},
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N. V. Tsilevich. Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 111-132. http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a8/