Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra

Abstract

The higher rank Askey-Wilson algebra was recently constructed in the $n$-fold tensor product of $U_q({\mathfrak{sl}}_2)$. In this paper we prove a class of identities inside this algebra, which generalize the defining relations of the rank one Askey-Wilson algebra. We extend the known construction algorithm by several equivalent methods, using a novel coaction. These allow to simplify calculations significantly. At the same time, this provides a proof of the corresponding relations for the higher rank $q$-Bannai-Ito algebra.

References in corpus (3)

• The Universal Askey-Wilson Algebra
• Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra
• Revisiting the Askey--Wilson algebra with the universal R-matrix of $U_q(sl(2))$

Cited by in corpus (7)

• The Askey-Wilson algebra and its avatars
• Representations of the rank two Racah algebra and orthogonal multivariate polynomials
• Revisiting the Askey--Wilson algebra with the universal R-matrix of $U_q(sl(2))$
• An Askey-Wilson Algebra of Rank 2
• Higher Rank Askey-Wilson Algebras as Skein Algebras
• Chern-Simons theory, link invariants and the Askey-Wilson algebra
• Factorized $A_2$-Leonard pair