NONLINEAR SCHRODINGER MODEL WITH BOUNDARY, INTEGRABILITY AND SCATTERING MATRIX BASED ON THE DEGENERATE AFFINE HECKE ALGEBRA

The delta-function interacting many-body systems (nonlinear Schrodinge r models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these int egrable operators. This method is based on the infinite-dimensional re presentation for solutions of the classical Yang-Baxter equation and t he classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schrodinger model are investigated.