The Equitable Presentation of $${\mathfrak{osp}_q(1|2)}$$ 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 $${q\rightarrow -q}$$ . A q-analog of the Bannai–Ito algebra is shown to arise as the covariance algebra of $${\mathfrak{osp}_q(1|2)}$$ .