Integrable spin Calogero-Moser systems

Details Integrable spin Calogero-Moser systems Integrable spin Calogero-Moser systems

2001-05-19

arxiv.org/abs/math/0105162v1

Commun.Math.Phys. 231 (2002) 257-286

Mathematics

Quantum Algebra

30 pages, Latex file

Scientific paper

10.1007/s00220-002-0724-1

We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. The associated integrable models (called integrable spin Calogero-Moser systems in the paper) and their Lax pairs are then obtained via Poisson reduction and gauge transformations. For Lie algebras of $A_{n}$-type, this new class of integrable systems includes the usual Calogero-Moser systems as subsystems. Our method is guided by a general framework which we develop here using dynamical Lie algebroids.

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