Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 115, 30 pages      arXiv:2407.10404      https://doi.org/10.3842/SIGMA.2024.115

On the Higher-Rank Askey-Wilson Algebras

Wanxia Wang and Shilin Yang
School of Mathematics, Statistics and Mechanics, Beijing University of Technology, P.R. China

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

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 $\mathfrak{aw}(n)$.

Key words: Askey-Wilson algebra; braid group.

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