Quantum inverse scattering method for the q-boson model and symmetric functions

Details Quantum inverse scattering method for the q-boson model and symmetric functions Quantum inverse scattering method for the q-boson model and symmetric functions

2005-10-20

arxiv.org/abs/math-ph/0510073v1

Physics

Mathematical Physics

13 pages. To appear in Funct. Anal. Appl

Scientific paper

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.

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