Abstract:
It is well known that scattering of particles in the Calogero model, which recently drew attention in connection with $c=1$ strings and integrable models in statistical mechanics, is reduced to
two-particle collisions. It follows from Harish-Chandra and Gindikin–Karpelevich results, related to the harmonic analysis on simple Lie groups. Unfortunately their formulae don't work if particles form clusters in the asymptotics. We reformulate their results in a form which
allows to apply them to this situation. The scattering of clusters is also factorizible, but depends on structures of constituents. In conclusion we discuss a similar problem in the deformed Calogero model related to quantum groups, which describes also interactions of excited states
in the XXZ-model.
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