Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra

Abstract

The $s{l}_N$-Onsager algebra has been introduced by Uglov and Ivanov in 1995. In this letter, a FRT presentation of the $s{l}_N$-Onsager algebra is given, its current algebra and commutative subalgebra are constructed. Certain quotients of the $s{l}_N$-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.

arXiv comment13 pages

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• Generalised Onsager Algebra in Quantum Lattice Models
• Quantum spin chains from Onsager algebras and reflection $K$-matrices
• The $q$-Bannai-Ito algebra and multivariate $(-q)$-Racah and Bannai-Ito polynomials