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SIGMA, 2024 Volume 20, 115, 30 pp. (Mi sigma2117)

On the Higher-Rank Askey–Wilson Algebras

Wanxia Wang, Shilin Yang

School of Mathematics, Statistics and Mechanics, Beijing University of Technology, P.R. China

Abstract: In the paper, the algebra $\mathscr{A}(n)$, which is generated by an upper triangular generating matrix with triple relations, is introduced. It is shown that there exists an isomorphism between the algebra $\mathscr{A}(n)$ and the higher-rank Askey–Wilson algebra $\mathfrak{aw}(n)$ introduced by Crampé et al. Furthermore, we establish a series of automorphisms of $\mathscr{A}(n)$, which satisfy braid group relations and coincide with those in $\mathfrak{aw}(n)$.

Keywords: Askey–Wilson algebra, braid group.

MSC: 20F36, 33D45, 81R12

Received: July 16, 2024; in final form December 15, 2024; Published online December 28, 2024

Language: English

DOI: 10.3842/SIGMA.2024.115


ArXiv: 2407.10404


© Steklov Math. Inst. of RAS, 2025