On the Higher-Rank Askey-Wilson Algebras
Wanxia Wang, Shilin Yang

TL;DR
This paper introduces a new algebra $\
Contribution
It establishes an isomorphism between the algebra $\\mathscr{A}(n)$ and the higher-rank Askey-Wilson algebra $\\mathfrak{aw}(n)$, and explores its automorphisms.
Findings
Proves the isomorphism between $\\mathscr{A}(n)$ and $\\mathfrak{aw}(n)$.
Identifies automorphisms satisfying braid group relations.
Connects algebraic structures with braid group symmetries.
Abstract
In the paper, the algebra , 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 and the higher-rank Askey-Wilson algebra introduced by Cramp\'e et al. Furthermore, we establish a series of automorphisms of , which satisfy braid group relations and coincide with those in .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Algebraic structures and combinatorial models
