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Quantum Dynamical R-matrices and Quantum Frobenius Group
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abstract
We propose an algebraic scheme for quantizing the rational Ruijsenaars-Schneider model in the R-matrix formalism. We introduce a special parameterization of the cotangent bundle over GL(N,C). In new variables the standard symplectic structure is described by a classical (Frobenius) r-matrix and by a new dynamical $\bar{r}$-matrix. Quantizing both of them we find the quantum L-operator algebra and construct its particular representation corresponding to the rational Ruijsenaars-Schneider system. Using the dual parameterization of the cotangent bundle we also derive the algebra for the L-operator of the trigonometric Calogero-Moser system.
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Spin Ruijsenaars-Schneider models are Coulomb branches
Cohomological and K-theoretic Coulomb branches of necklace quivers are shown to provide the Poisson structures and Hamiltonians that generate the rational and hyperbolic spin Ruijsenaars–Schneider equations of motion.
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