TY - JOUR

T1 - Quantum inverse scattering method for the q-boson model and symmetric functions

AU - Tsilevich, N. V.

PY - 2006/7/1

Y1 - 2006/7/1

N2 - 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).

AB - 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).

KW - Hall-Littlewood functions

KW - Phase model

KW - q-boson model

KW - Quantum inverse scattering method

KW - Schur functions

KW - Symmetric functions

UR - http://www.scopus.com/inward/record.url?scp=33749537065&partnerID=8YFLogxK

U2 - 10.1007/s10688-006-0032-1

DO - 10.1007/s10688-006-0032-1

M3 - Article

AN - SCOPUS:33749537065

VL - 40

SP - 207

EP - 217

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 3

ER -