Quantum Dynamical Rmatrices and Quantum Frobenius Group
Abstract
We propose an algebraic scheme for quantizing the rational RuijsenaarsSchneider model in the Rmatrix 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) rmatrix and by a new dynamical $\bar{r}$matrix. Quantizing both of them we find the quantum Loperator algebra and construct its particular representation corresponding to the rational RuijsenaarsSchneider system. Using the dual parameterization of the cotangent bundle we also derive the algebra for the Loperator of the trigonometric CalogeroMoser system.
 Publication:

eprint arXiv:qalg/9610009
 Pub Date:
 October 1996
 DOI:
 10.48550/arXiv.qalg/9610009
 arXiv:
 arXiv:qalg/9610009
 Bibcode:
 1996q.alg....10009A
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 latex, 15 pages, the statement about the form of the quantum integrals of motion is corrected