@article{9a5e3e9d25424748a1fb21de4138e270,

title = "On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model",

abstract = "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 An type. A connection with the dynamical R-matrix approach is discussed.",

keywords = "Quantum L-operator, Trigonometric Ruijsenaars model, Vertex-face correspondence",

author = "A. Antonov and K. Hasegawa and A. Zabrodin",

note = "Funding Information: We are grateful to A. Alekseev, G. Arutyunov, J. Avan, A. Belavin, E. BiUey, L. Chekhov, H.J. de Vega, B. Enriquez, L. Faddeev, B. Feigin, S. Frolov, P. Kulish, J.M. Maillard, T. Miwa, N. Reshetikhin, S. Sergeev, F. Smirnov, Yu. Stroganov, C.M. Viallet for fruitful discussions and comments. A.A. is thankful to L. Baulieu and Laboratoire de Physique Th6orique et Hautes I~nergies, Paris, France for hospitality. A.A. also would like to thank O. Babelon for the great help and interest in this work. A.A. thanks M. Coulon for encouragement. Some results of this work were reported by the first author in the talk given on the Semester {"}Syst~mes int6grables{"}, September 15, 1996-February 14, 1997, Centre Emile Borel, Institut Henri Poincar6, Paris, France. The work of A.Z. was supported in part by RFBR grant 97-02-19085 and by ISTC grant 015. K.H. acknowledges the hospitality at Centre de Recherche Mathematique and Universit6 de Montr6al during his visit and especially thanks Professor J.E van Diejen.",

year = "1997",

month = oct,

day = "20",

doi = "10.1016/S0550-3213(97)00520-8",

language = "English",

volume = "503",

pages = "747--770",

journal = "Nuclear Physics B",

issn = "0550-3213",

publisher = "Elsevier",

number = "3",

}