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

Abstract : 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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Submitted on : Monday, November 19, 2018 - 2:27:01 PM
Last modification on : Friday, November 27, 2020 - 1:30:01 PM

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Pascal Baseilhac, Nicolas Crampé, Rodrigo A. Pimenta. Higher rank classical analogs of the Askey-Wilson algebra from the $sl_N$ Onsager algebra. Journal of Mathematical Physics, American Institute of Physics (AIP), 2019, 60 (8), pp.081703. ⟨10.1063/1.5111292⟩. ⟨hal-01926766⟩

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