  The trigonometric Ruijsenaars-Schneider model is derived by symplectic
reduction of Poisson-Lie symmetric free motion on the group U(n). The commuting
flows of the model are effortlessly obtained by reducing canonical free flows
on the Heisenberg double of U(n). The free flows are associated with a very
simple Lax matrix, which is shown to yield the Ruijsenaars-Schneider Lax matrix
upon reduction.
