R-MATRIX QUANTIZATION OF THE ELLIPTIC RUIJSENAARS-SCHNEIDER MODEL

It is shown that the classical L-operator algebra of the elliptic Ruij senaars-Schneider model can be realized as a subalgebra of the algebra of functions on the cotangent bundle over the centrally extended curr ent group in two dimensions. It is governed by two dynamic r and (r) o ver bar-matrices satisfying a closed system of equations. The correspo nding quantum R- and (R) over bar-matrices are found as solutions to q uantum analogues of these equations. We present the quantum L-operator algebra and show that the system of equations for R and (R) over bar arises as the compatibility condition for this algebra. It turns out t hat the R-matrix is twist-equivalent to the Felder elliptic R-F-matrix , with (R) over bar playing the role of the twist. The simplest repres entation of the quantum L-operator algebra corresponding to the ellipt ic Ruijsenaars-Schneider model is obtained. The connection of the quan t um L-operator algebra to the fundamental relation (RLL)-L-B = LLRB w ith the Belavin elliptic R-matrix is established. As a by-product of o ur construction, we find a new N-parameter elliptic solution to the cl assical Yang-Baxter equation.