C(2)N+1 Ruijsenaars-Schneider models
Jean Avan, Genevieve Rollet
Abstract
We define the notion of C(2)N+1 Ruijsenaars-Schneider models and construct their Lax formulation. They are obtained by a particular folding of the A2N+1 systems. Their commuting Hamiltonians are linear combinations of Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for specific values of the exponential one-body couplings but with the most general 2 double-poles structure as opposed to the formerly studied BCN case. Extensions to the elliptic potentials are briefly discussed.
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