Higher rank classical analogs of the Askey-Wilson algebra from the sl(N) Onsager algebra

Author(s)

Baseilhac, Pascal ^[1] ; Crampe, Nicolas ^{[1, 2, 3]} ; Pimenta, Rodrigo A. ^{[4, 5, 1]}

Affiliation

^[1] Univ Orleans, Univ Tours, CNPS UMR 7013, Inst Denis Poisson, Parc Crammont, F-37200 Tours - France

^[2] Univ Montpellier, CNRS, L2C, Montpellier - France

^[3] Univ Montreal, FRANCE Ctr Rech Math, CNRS, POB 6128, Montreal, PQ H3C 3J7 - Canada

^[4] Minist Educ Brazil, CAPES Fdn, BR-70040020 Brasilia, DF - Brazil

^[5] Univ Sao Paulo, Inst Fis Sao Carlos, Caixa Postal 369, BR-13560590 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 60, n. 8 AUG 2019.
• Web of Science Citations: 0

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, and its current algebra and commutative subalgebra are constructed. Certain quotients of the sl(N)-Onsager algebra are then considered, which produce classical (q = 1) analogs of higher rank extensions of the Askey-Wilson algebra. As examples, the cases N = 3 and N = 4 are described in detail. (AU)

• FAPESP's process: 17/02987-8 - New developments in quantum spin chains
• Grantee: Rodrigo Alves Pimenta
• Support Opportunities: Scholarships in Brazil - Post-Doctoral