Universal R-matrix formalism for the spin Calogero-Moser system and its difference counterpart

The expression of the quantum Ruijsenaars-Schneider Hamiltonian is obtained in the framework of the dynamical $R$-matrix formalism. This generalizes to the case of $U_q(s{l}_n)$ the result obtained by O. Babelon, D. Bernard and E. Billey for $U_q(s{l}_2)$ which is the higher difference Lame operator. The general method involved is the universal $R$-matrix construction.