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arXiv · 1502.01297

The equitable presentation of $\mathfrak{osp}_q(1|2)$ and a $q$-analog of the Bannai-Ito algebra

Vincent X. Genest·Luc Vinet·Alexei Zhedanov
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Abstract

The equitable presentation of the quantum superalgebra $\mathfrak{osp}_q(1|2)$, in which all generators appear on an equal footing, is exhibited. It is observed that in their equitable presentations, the quantum algebras $\mathfrak{osp}_q(1|2)$ and $\mathfrak{sl}_q(2)$ are related to one another by the formal transformation $q\rightarrow -q$. A $q$-analog of the Bannai-Ito algebra is shown to arise as the covariance algebra of $\mathfrak{osp}_q(1|2)$.

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Vincent X. Genest, Luc Vinet, Alexei Zhedanov. 2015-02-04. The equitable presentation of $\mathfrak{osp}_q(1|2)$ and a $q$-analog of the Bannai-Ito algebra. https://doi.org/10.1007/s11005-015-0795-5

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