2 problems

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Arutyunov–Frolov Poisson-bracket conjecture for the trigonometric spin Ruijsenaars–Schneider system
Arutyunov–Frolov conjecture. The phase space admits the stated Poisson bracket, with
Conjectureopenintegrable-systems poisson-geometry ruijsenaars-schneider-systemsarXiv posted 2 days ago
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Gorsky–Nekrasov conjecture on the Heisenberg-double derivation of the trigonometric real form
The trigonometric real form called the $\mathrm{III}_{\mathrm{b}}$ system is obtained from gauged WZW theory. Gorsky–Nekrasov conjecture. It should be possible to derive the same s…
Conjectureopenintegrable-systems poisson-lie-groups ruijsenaars-schneider-systemsarXiv posted 2 days ago

Arutyunov–Frolov Poisson-bracket conjecture for the trigonometric spin Ruijsenaars–Schneider system