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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Genest, V.X., Vinet, L. & Zhedanov, A. The Equitable Presentation of \({\mathfrak{osp}_q(1|2)}\) and a q-Analog of the Bannai–Ito Algebra. Lett Math Phys 105, 1725–1734 (2015). https://doi.org/10.1007/s11005-015-0795-5
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DOI: https://doi.org/10.1007/s11005-015-0795-5