A class of Calogero type reductions of free motion on a simple Lie group

Details A class of Calogero type reductions of free motion on a simple Lie group A class of Calogero type reductions of free motion on a simple Lie group

2006-09-29

arxiv.org/abs/math-ph/0609085v2

Lett.Math.Phys.79:263-277,2007

Physics

Mathematical Physics

shortened to 13 pages in v2 on request of Lett. Math. Phys. and corrected some spelling errors

Scientific paper

10.1007/s11005-007-0146-2

The reductions of the free geodesic motion on a non-compact simple Lie group G based on the $G_+ \times G_+$ symmetry given by left- and right multiplications for a maximal compact subgroup $G_+ \subset G$ are investigated. At generic values of the momentum map this leads to (new) spin Calogero type models. At some special values the `spin' degrees of freedom are absent and we obtain the standard $BC_n$ Sutherland model with three independent coupling constants from SU(n+1,n) and from SU(n,n). This generalization of the Olshanetsky-Perelomov derivation of the $BC_n$ model with two independent coupling constants from the geodesics on $G/G_+$ with G=SU(n+1,n) relies on fixing the right-handed momentum to a non-zero character of $G_+$. The reductions considered permit further generalizations and work at the quantized level, too, for non-compact as well as for compact G.

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