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We report on the the trigonometric spin Ruijsenaars--Sutherland hierarchy derived recently by Poisson reduction of a bi-Hamiltonian hierarchy associated with free geodesic motion on the Lie group U(n). In particular, we give a direct proof of a previously stated result about the form of the second Poisson bracket in terms of convenient variables.

trends in mathematics

On the bi-Hamiltonian Structure of the Trigonometric Spin Ruijsenaars–Sutherland Hierarchy

pdf-texts/10.1007_978-3-030-53305-2_5.txt