Tensor operators and Wigner-Eckart theorem for the quantum superalgebra U_{q}[osp(1\mid 2)]

TL;DR

This paper develops tensor operators within graded representations of the quantum superalgebra U_{q}[osp(1|2)] and proves a Wigner-Eckart theorem, providing explicit examples and calculations of matrix elements.

Contribution

It introduces the concept of tensor operators in graded Hopf algebra representations and establishes a Wigner-Eckart theorem for U_{q}[osp(1|2)], including explicit examples and calculations.

Findings

Wigner-Eckart theorem proven for U_{q}[osp(1|2)]

Explicit reduced matrix elements calculated

Construction of elements in the center of the algebra

Abstract

Tensor operators in graded representations of Z_{2}-graded Hopf algebras are defined and their elementary properties are derived. Wigner-Eckart theorem for irreducible tensor operators for U_{q}[osp(1\mid 2)] is proven. Examples of tensor operators in the irreducible representation space of Hopf algebra U_{q}[osp(1\mid 2)] are considered. The reduced matrix elements for the irreducible tensor operators are calculated. A construction of some elements of the center of U_{q}[osp(1\mid 2)] is given.