Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-12-25
Physics
High Energy Physics
High Energy Physics - Theory
latex, 29 pages, some misprints are corrected and the meromorphic version of the quantum L-operator algebra is discussed
Scientific paper
10.1007/BF02634266
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.
Arutyunov G. E.
Chekhov L. O.
Frolov S. A.
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