Quantum Dynamical R-matrices and Quantum Frobenius Group
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.
- Publication:
-
eprint arXiv:q-alg/9610009
- Pub Date:
- October 1996
- DOI:
- 10.48550/arXiv.q-alg/9610009
- arXiv:
- arXiv:q-alg/9610009
- Bibcode:
- 1996q.alg....10009A
- Keywords:
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- Mathematics - Quantum Algebra;
- High Energy Physics - Theory;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- latex, 15 pages, the statement about the form of the quantum integrals of motion is corrected