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

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 $q\to -q$. 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