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

Symmetry Integrability and Geometry-Methods and Applications

article

Hadewijch DE CLERCQ¹ 

[1] Department of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University

关键词: Askey–Wilson algebra;    Bannai–Ito algebra;   

DOI  :  10.3842/SIGMA.2019.099

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown