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 $P_\lambda(x;q^2)$.
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
\Bibitem{Tsi06}
\by N.~V.~Tsilevich
\paper Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions
\jour Funktsional. Anal. i Prilozhen.
\yr 2006
\vol 40
\issue 3
\pages 53--65
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\jour Funct. Anal. Appl.
\yr 2006
\vol 40
\issue 3
\pages 207--217
\crossref{https://doi.org/10.1007/s10688-006-0032-1}
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https://www.mathnet.ru/eng/faa743
https://doi.org/10.4213/faa743
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