Quantum Dynamical R-matrices and Quantum Frobenius Group
q-alg
2016-09-08 v2 高能物理 - 理论
量子代数
可精确求解与可积系统
solv-int
摘要
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 -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.
关键词
引用
@article{arxiv.q-alg/9610009,
title = {Quantum Dynamical R-matrices and Quantum Frobenius Group},
author = {G. E. Arutyunov and S. A. Frolov},
journal= {arXiv preprint arXiv:q-alg/9610009},
year = {2016}
}
备注
latex, 15 pages, the statement about the form of the quantum integrals of motion is corrected