dorsal/arxiv
View SchemaR-matrix Quantization of the Elliptic Ruijsenaars--Schneider model
| Authors | G. E. Arutyunov, L. O. Chekhov, S. A. Frolov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9612032 |
| URL | https://arxiv.org/abs/q-alg/9612032 |
| DOI | 10.1007/BF02634266 |
Abstract
It is shown that the classical L-operator algebra of the elliptic Ruijsenaars-Schneider model can be realized as a subalgebra of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions. It is governed by two dynamical r and $\bar{r}$-matrices satisfying a closed system of equations. The corresponding quantum R and $\overline{R}$-matrices are found as solutions to quantum analogs of these equations. We present the quantum L-operator algebra and show that the system of equations on R and $\overline{R}$ arises as the compatibility condition for this algebra. It turns out that the R-matrix is twist-equivalent to the Felder elliptic R^F-matrix with $\overline{R}$ playing the role of the twist. The simplest representation of the quantum L-operator algebra corresponding to the elliptic Ruijsenaars-Schneider model is obtained. The connection of the quantum L-operator algebra to the fundamental relation RLL=LLR with Belavin's elliptic R matrix is established. As a byproduct of our construction, we find a new N-parameter elliptic solution to the classical Yang-Baxter equation.
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"abstract": "It is shown that the classical L-operator algebra of the elliptic\nRuijsenaars-Schneider model can be realized as a subalgebra of the algebra of\nfunctions on the cotangent bundle over the centrally extended current group in\ntwo dimensions. It is governed by two dynamical r and $\\bar{r}$-matrices\nsatisfying a closed system of equations. The corresponding quantum R and\n$\\overline{R}$-matrices are found as solutions to quantum analogs of these\nequations. We present the quantum L-operator algebra and show that the system\nof equations on R and $\\overline{R}$ arises as the compatibility condition for\nthis algebra. It turns out that the R-matrix is twist-equivalent to the Felder\nelliptic R^F-matrix with $\\overline{R}$ playing the role of the twist. The\nsimplest representation of the quantum L-operator algebra corresponding to the\nelliptic Ruijsenaars-Schneider model is obtained. The connection of the quantum\nL-operator algebra to the fundamental relation RLL=LLR with Belavin\u0027s elliptic\nR matrix is established. As a byproduct of our construction, we find a new\nN-parameter elliptic solution to the classical Yang-Baxter equation.",
"arxiv_id": "q-alg/9612032",
"authors": [
"G. E. Arutyunov",
"L. O. Chekhov",
"S. A. Frolov"
],
"categories": [
"q-alg",
"hep-th",
"math.QA",
"nlin.SI",
"solv-int"
],
"doi": "10.1007/BF02634266",
"title": "R-matrix Quantization of the Elliptic Ruijsenaars--Schneider model",
"url": "https://arxiv.org/abs/q-alg/9612032"
},
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