QUANTUM DYNAMICAL R-MATRICES AND QUANTUM FROBENIUS GROUP

We propose an algebraic scheme for quantizing the rational Ruijsenaars -Schneider model in the R-matrix formalism. We introduce a special par ametrization of the cotangent bundle over GL(N, C). In new variables t he standard symplectic structure is described by a classical (Frobeniu s) tau-matrix and by a new dynamical <(tau)over bar>-matrix. Quantizin g both of them we find the quantum L-operator algebra and construct it s particular representation corresponding to the rational Ruijsenaars- Schneider system. Using the dual parametrization of the cotangent bund le we also derive the algebra for the L-operator of the hyperbolic Cal ogero-Moser system.