The nondynamical r-matrix for the Ruijsenaars–Schneider model and the classical Sklyanin algebra

✍ Scribed by Bo-yu Hou; Wen-li Yang

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 57 KB
• Volume: 261
• Category: Article
• ISSN: 0375-9601
• DOI: 10.1016/s0375-9601(99)00645-3

✦ Synopsis

Through a gauge transformation depending on the dynamical variables q , we find the factorized Lax-operator for the i Ž . elliptic Ruijsenaars-Schneider RS model. It is shown that the RS model and its nonrelativistic version, Calogero-Moser model, is governed by the exact same nondynamical r-matrix -the classical Z -symmetric r-matrix. The corresponding n Ž . Lax-operator can be expressed in terms of the spectrum independent operators S i.e. the classical Sklyanin algebra .

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