DEGENERATE AFFINE HECKE ALGEBRAS AND TWO-DIMENSIONAL PARTICLES

We demonstrate that the quantization of momenta in different two dimensional theories of elementary particles with factorizable scattering amplitudes gives the so-called degenerate affine Hecke algebras and their versions. Some connections with quantum groups(Yangians), the two-dimensional conformal field theory and representation theory am discussed. In particular, an interpretation and generalizations of the difference counterpart of the Knizhnik-Zamolodchikov equation are found by means of the particles on a segment.