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 Uq(sl₂). 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 for simplifying calculations significantly. At the same time, this provides proof of the corresponding relations for the higher rank q-Bannai-Ito algebra.