SCATTERING OF CLUSTERS IN QUANTUM CALOGERO MODEL

It is well known that scattering of particles in the Calogero model, w hich recently drew attention in connection with c = 1 strings and inte grable models in statistical mechanics, is reduced to two-particle col lisions. It follows from Harish-Chandra and Gindikin-Karpelevich resul ts, which are related to the harmonic analysis on simple Lie groups. U nfortunately their formulae don't work if particles form clusters in t he asymptotics. We reformulate their results in a form which allows to apply them to this situation. The scattering of clusters is also fact orizible, but depends on structures of constituents. In conclusion we discuss a similar problem in the deformed Calogero model related to qu antum groups, which describes also interactions of excited states in t he XXZ-model.