  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 is essentially the operator
of multiplication by the generating function of the complete homogeneous
symmetric functions, and the wave functions are expressed in terms of the Schur
functions. The general case of the q-boson model is related in the same way to
the Hall-Littlewood symmetric functions.
