On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model

We elaborate 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 An type. A connection with the dynamical R-matrix approach is discussed. LPTHE 97-09 Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Tour 16 1 étage, 4 place Jussieu, 75252 Paris cedex 05-France and Landau Institute for Theoretical Physics Kosygina str. 2, 117940 Moscow, Russia, e-mail: [email protected] Mathematical Institute, Tohoku University, Sendai JAPAN, e-mail: [email protected] Joint Institute of Chemical Physics, Kosygina str. 4, 117334, Moscow, Russia and ITEP, 117259, Moscow, Russia, e-mail: [email protected]