On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijs']jsenaars model

We elaborate on the trigonometric Version of intertwining Vectors and factorized L-operators. The starting point is the corresponding elliptic construction with Belavin's R-matrix. The naive trigonometric limit is singular and a careful analysis is needed. It is shown that the construction admits several different trigonometric degenerations. As a by-product, a quantum Lax operator for the trigonometric Ruijsenaars model intertwined by a non-dynamical R-matrix is obtained. The latter differs from the standard trigonometric R-matrix of A(n) type. A connection with the dynamical R-matrix approach is discussed. (C) 1997 Elsevier Science B.V. PACS: 11.10.-z.