Canonical basis for quantum osp(1|2)

TL;DR

This paper constructs and analyzes the canonical basis for the quantum superalgebra osp(1|2), providing a foundational example for quantum superalgebras and relating it to the well-known sl(2) case.

Contribution

It introduces the first example of a canonical basis for a quantum superalgebra, specifically for osp(1|2), and relates it to the sl(2) case.

Findings

Constructed the canonical basis for quantum osp(1|2)

Related the basis to the canonical basis for sl(2)

Provided a new example of canonical basis for quantum superalgebras

Abstract

We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra osp(1|2). Then we formulate and compute the corresponding canonical bases, and relate them to the counterpart for sl(2). This provides a first example of canonical basis for quantum superalgebras.