Quantum trace formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model

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.
The talk is based on recent paper
https://arxiv.org/abs/1902.06755