Abstract
The reductions of the free geodesic motion on a non-compact simple Lie group G based on the G + × 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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Fehér, L., Pusztai, B.G. A Class of Calogero Type Reductions of Free Motion on a Simple Lie Group. Lett Math Phys 79, 263–277 (2007). https://doi.org/10.1007/s11005-007-0146-2
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DOI: https://doi.org/10.1007/s11005-007-0146-2