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This article is cited in 37 scientific papers (total in 37 papers)
Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions
N. V. Tsilevich
St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
The purpose of this paper is to show that the quantum inverse scattering method for the so-called $q$-boson model has a nice interpretation in terms of the algebra of symmetric functions. In particular, in the case of the
phase model (corresponding to $q=0$) the creation operator coincides (modulo a scalar factor) with the operator of
multiplication by the generating function of complete homogeneous symmetric functions, and the wave functions are expressed via the Schur functions $s_\lambda(x)$. The general case of the $q$-boson model is related in a similar way to the Hall–Littlewood symmetric functions $P_\lambda(x;q^2)$.
Keywords:
$q$-boson model, phase model, quantum inverse scattering method, symmetric functions, Hall–Littlewood functions, Schur functions
DOI:
https://doi.org/10.4213/faa743
 Full text:
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English version:
Functional Analysis and Its Applications, 2006, 40:3, 207–217
Bibliographic databases:
    
UDC:
517.958
Received: 10.08.2005
Citation:
N. V. Tsilevich, “Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 53–65; Funct. Anal. Appl., 40:3 (2006), 207–217
Citation in format AMSBIB
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