A class of integrable spin Calogero-Moser systems. II: Exact solvability. (English) Zbl 1110.37044

Li, Luen-chau

IMRP, Int. Math. Res. Pap. 2006, No. 13, Article ID 62058, 53 p. (2006).

Summary: In part I [the author, Commun. Math. Phys. 231, 257–286 (2002; Zbl 1012.37034)], we introduced a class of integrable spin Calogero-Moser systems associated with the classical dynamical \(r\)-matrices with spectral parameter. Here, the main purpose is to give explicit solutions of several factorization problems associated with infinite-dimensional Lie groupoids which allow us to write down the solutions of these integrable models.

MSC:

37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70G65	Symmetries, Lie group and Lie algebra methods for problems in mechanics
70H06	Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
81R12	Groups and algebras in quantum theory and relations with integrable systems
81V70	Many-body theory; quantum Hall effect
17B20	Simple, semisimple, reductive (super)algebras

Keywords:

explicit solutions; factorization problems; infinite-dimensional Lie groupoids; integrable models

Citations:

Zbl 1012.37034