On the Higher-Rank Askey-Wilson Algebras

Abstract

In the paper, the algebra 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 𝒜(𝑛) and the higher-rank Askey-Wilson algebra 𝖆𝖜(𝑛) introduced by Crampé et al. Furthermore, we establish a series of automorphisms of 𝒜(𝑛), which satisfy braid group relations and coincide with those in 𝖆𝖜(𝑛).