The equitable presentation of $\mathfrak{osp}_q(1|2)$ and a $q$-analog of the Bannai-Ito algebra
arXiv:1502.01297 · doi:10.1007/s11005-015-0795-5
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 $\mathfrak{osp}_q(1|2)$.
8-page Letter