# Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond

## TL;DR

This paper algebraically determines Wigner coefficients for Lie superalgebra gl(m|n) unitary representations using Casimir invariants, explores non-unitary cases, and reveals symmetry relations between coefficient classes.

## Contribution

It introduces a method to compute Wigner coefficients algebraically for gl(m|n) and extends analysis to non-unitary representations, revealing new symmetry relations.

## Key findings

- Wigner coefficients are derived using eigenvalues of Casimir invariants.
- Symmetry relations between different classes of Wigner coefficients are established.
- Extensions to non-unitary representations are explored.

## Abstract

In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary representations of the Lie superalgebra gl(mjn). Extensions to the non-unitary case are investigated. A symmetry relation between two classes of Wigner coefficients is given in terms of a ratio of dimensions.