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

TL;DR

This paper presents an equitable presentation of the quantum superalgebra _q(1|2), explores its relation to _q(2) via a q-transform, and introduces a q-analog of the Bannai-Ito algebra as its covariance algebra.

Contribution

It introduces an equitable presentation of _q(1|2), revealing its relation to _q(2) through a q-transformation, and defines a new q-analog of the Bannai-Ito algebra.

Findings

Equitable presentation of _q(1|2) is established.

Relation between _q(1|2) and _q(2) via q  transformation is observed.

A q-analog of the Bannai-Ito algebra is derived as a covariance 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 $\mathfrak{osp}_q(1|2)$.