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Quantum Trace Formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model
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We conjecture the quantum analogue of the classical trace formulae for the integrals of motion of the quantum hyperbolic Ruijsenaars-Schneider model. This is done by departing from the classical construction where the corresponding model is obtained from the Heisenberg double by the Poisson reduction procedure. We also discuss some algebraic structures associated to the Lax matrix in the classical and quantum theory which arise upon introduction of the spectral parameter.
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Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$ to spin Ruijsenaars--Sutherland models
The trigonometric spin Ruijsenaars-Sutherland hierarchy is obtained by Poisson reduction of a bi-Hamiltonian free system on T*U(n), yielding explicit compatible reduced Poisson brackets.
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