, Volume 212, Issue 2, pp 297-321

Factorization Dynamics and Coxeter--Toda Lattices

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Abstract:

It is shown that the factorization relation on simple Lie groups with standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can be regarded as a discretization of the Toda flow. In case of SL n the integrals of the factorization dynamics are integrals of the relativistic Toda system. A substantial part of the paper is devoted to the description of symplectic leaves in simple complex Lie groups, its Borel subgroups and their doubles.

Received: 1 October 1999 / Accepted: 18 January 2000