Structures in BC_N Ruijsenaars-Schneider models

Details Structures in BC_N Ruijsenaars-Schneider models Structures in BC_N Ruijsenaars-Schneider models

2001-06-13

arxiv.org/abs/nlin/0106015v1

J.Math.Phys. 43 (2002) 403-416

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, gzip latex file

Scientific paper

10.1063/1.1423766

We construct the classical r-matrix structure for the Lax formulation of BC_N Ruijsenaars-Schneider systems proposed in hep-th 0006004. The r-matrix structure takes a quadratic form similar to the A_N Ruijsenaars-Schneider Poisson bracket behavior, although the dynamical dependence is more complicated. Commuting Hamiltonians stemming from the BC_N Ruijsenaars-Schneider Lax matrix are shown to be linear combinations of particular Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for specific values of the exponential one-body couplings. Uniqueness of such commuting Hamiltonians is established once the first of them and the general analytic structure are given.

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