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 sλ(x). The general case of the q-boson model is related in a similar way to the Hall-Littlewood symmetric functions Pλ(x;q2).
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