## R-matrix quantization of the elliptic Ruijsenaars-Schneider model

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**Citation: **

*G. E. Arutyunov, L. O. Chekhov and S. A. Frolov, R-matrix quantization of the elliptic Ruijsenaars-Schneider model, Communications in Mathematical Physics, 192, 1998, 405-432*

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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 RF -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.

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**Author's Homepage: **

http://people.tcd.ie/frolovs
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**Description: **

PUBLISHED
**Author:**FROLOV, SERGEY

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**Publisher: **

Springer Verlag
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**Type of material: **

Journal Article#####
**Series/Report no: **

Communications in Mathematical Physics;192;

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**Availability: **

Full text available#####
**Keywords: **

Mathematics, Ruijsenaars-Schneider model
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