Geodesic
Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 53-65

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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 $P_\lambda(x;q^2)$.
Mots-clés : $q$-boson model
Keywords: phase model, quantum inverse scattering method, symmetric functions, Hall–Littlewood functions, Schur functions. 
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     author = {N. V. Tsilevich},
     title = {Quantum {Inverse} {Scattering} {Method} for the $q${-Boson} {Model} and {Symmetric} {Functions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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N. V. Tsilevich. Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 53-65. http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a5/