A spin-shift relation of the Ruijsenaars-Schneider Hamiltonian of type $C_n$

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We constract a spin-shift relation of the trigonometric Ruijsenaars-Schneider Hamiltonian of type $C_n$. This is a succesive study of our previous paper whose title is " A Spin-Shift Operator of the Multi-particle Ruijsenaars-Schneider Hamiltonian" in Lett. Math. Phys. 60 pp.59-61, (2002).
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