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Higher rank classical analogs of the Askey-Wilson algebra from the $sl_N$ Onsager algebra
Journal article   Open access   Peer reviewed

Higher rank classical analogs of the Askey-Wilson algebra from the $sl_N$ Onsager algebra

Pascal Baseilhac, Nicolas Crampé and Rodrigo A. Pimenta
Journal of Mathematical Physics, Vol.60(8)
08/2019

Abstract

Onsager algebras Askey-Wilson algebra Yang-Baxter algebra Integrable systems MSC : 81R50; 81R10; 81U15
The $sl_N$-Onsager algebra has been introduced by Uglov and Ivanov in 1995. In this letter, a FRT presentation of the $sl_N$-Onsager algebra is given, its current algebra and commutative subalgebra are constructed. Certain quotients of the $sl_N$-Onsager algebra are then considered, which produce `classical' analogs of higher rank extensions of the Askey-Wilson algebra. As examples, the cases $N=3$ and $N=4$ are described in details.
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