R-matrix quantization of the elliptic Ruijsenaars-Schneider model
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, 405-432Download Item:
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.
Author's Homepage:
http://people.tcd.ie/frolovsDescription:
PUBLISHED
Author: FROLOV, SERGEY
Publisher:
Springer VerlagType of material:
Journal ArticleSeries/Report no:
Communications in Mathematical Physics;192;
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Full text availableKeywords:
Mathematics, Ruijsenaars-Schneider modelMetadata
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