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

Hadewijch De Clercq

发表信息：: SIGMA 15 (2019), 099, 32 pages
DOI：: 10.3842/SIGMA.2019.099

英文摘要：

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.

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