Scasimir operator, Scentre and Representations of U_q(osp(1|2))

TL;DR

This paper introduces a bosonic operator in U_q(osp(1|2)) that helps describe the center at roots of unity and simplifies classifying finite-dimensional irreducible representations.

Contribution

It presents a new bosonic operator that clarifies the center structure and representation classification in the quantum superalgebra U_q(osp(1|2)).

Findings

Bosonic operator anticommutes with fermionic generators.

Operator aids in describing the center at roots of unity.

Simplifies classification of finite-dimensional irreducible representations.

Abstract

A bosonic operator of U_q(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of U_q(osp(1|2)) for q a root of unity (in the unrestricted specialisation). As in the classical case, it also simplifies the classification of finite dimensional irreducible representations.