Abstract
Presentation of a method for generating Lax pairs for systems obtained by means of Hamiltonian reduction.
Similar content being viewed by others
References
Olshanetsky, M.A., Perelomov, A.M.: Classical integrable finite-dimensional systems related to Lie algebras. Phys. Rep. 71, 313–400 (1981)
Olshanetsky, M.A., Perelomov, A.M.: Completely integrable Hamiltonian systems connected with semisimple Lie algebras. Inv. Math. 37, 93–108 (1976)
Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian group actions and dynamical systems of Calogero type. Commun. Pure Appl. Math. 31, 481–507 (1978)
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)
Marshall, I.: A new model in the Calogero-Ruisenaars family. Commun. Math. Phys. 338, 563–587 (2015)
Alekseev, A.Yu., Malkin, A.Z.: Symplectic structures associated to Lie-Poisson groups. Commun. Math. Phys. 162, 147–174 (1994)
Fehér, L., Görbe, T.: The full phase space of a model in the Calogero–Ruijsenaars family. arXiv:1603.02877. (To appear in Jour. Geom. Phys.)
Reyman, A.G., Semenov-Tian-Shansky, M.A.: A new integrable case of the motion of the 4-dimensional rigid body. Commun. Math. Phys. 105, 461–472 (1986)
Reyman, A.G., Semenov-Tian-Shansky, M.A.: Lax representation with a spectral parameter for the Kowalewski top and its generalizations. Lett. Math. Phys. 14, 55–62 (1987)
Reyman, A.G.: Integrable Hamiltonian systems connected with graded Lie algebras. Differ. Geom. Lie Groups Mech. II. Zap. Nauchn. Semin. LOMI.95, 3–54 (1980). [J. Soviet Math. 19, 1507–1545 (1982)]
Acknowledgements
I would like to thank Andrei Zotov for useful discussions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Marshall, I. Spectral parameter dependent Lax pairs for systems of Calogero–Moser type. Lett Math Phys 107, 619–642 (2017). https://doi.org/10.1007/s11005-016-0912-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11005-016-0912-0
Keywords
- Integrable systems
- Hamiltonian reduction
- Poisson reduction
- Calogero model
- Ruijsenaars model
- Sutherland model