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

1997/04/29 by A. Antonov, K. Hasegawa, A. Zabrodin
Mathematics · Physics and Astronomy · #hep-th #math.QA #nlin.SI #q-alg #solv-int

paper · pdf · doi:10.1016/s0550-3213(97)00520-8

published as Nucl.Phys. B503 (1997) 747-770 · 20 pages, LaTeX, references are added

arxiv created 1997/04/29 · arxiv updated 2009/11/30

Abstract

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 A_n type. A connection with the dynamical R-matrix approach is discussed.

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