Letters in Mathematical Physics

, Volume 79, Issue 3, pp 263–277 | Cite as

A Class of Calogero Type Reductions of Free Motion on a Simple Lie Group

  • L. Fehér
  • B. G. Pusztai


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.

Mathematics Subject Classification (2000)

37J35 53D20 17B80 70G65 


Integrable systems Hamiltonian reduction Spin Calogero models BCn Sutherland model 


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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsMTA KFKI RMKIBudapestHungary
  2. 2.Department of Theoretical PhysicsUniversity of SzegedSzegedHungary
  3. 3.Centre de Recherches MathématiquesUniversité de MontréalMontrealCanada
  4. 4.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada

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