R-Matrix Quantization of the Elliptic
Ruijsenaars–Schneider Model |
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Authors: | GE Arutyunov LO Chekhov SA Frolov |
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Institution: | (1) Steklov Mathematical Institute, Gubkina 8, GSP-1, 117966, Moscow, Russia. E-mail: arut@genesis.mi.ras.ru; chekhov@genesis.mi.ras.ru; frolov@genesis.mi.ras.ru, RU |
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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 ?r-matrices satisfying a closed system of equations. The corresponding quantum R and ?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 ?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 ?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.
Received: 17 March 1997 / Accepted: 8 July 1997 |
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