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arXiv · 1908.11654

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

Hadewijch De Clercq
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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.

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BibTeXRIS

Hadewijch De Clercq. 2019-08-30. Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra. https://doi.org/10.3842/sigma.2019.099

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