Structures in BC_N Ruijsenaars-Schneider models

Abstract

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.

18 pages, gzip latex file

References in corpus (2)

• Quantum groupoids
• Integrability of the $C_n$ and $B{C}_n$ Ruijsenaars-Schneider models

Cited by in corpus (2)

• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• On Calogero-Francoise-type Lax matrices and their dynamical r-matrices