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

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 $gl\left(m\right|n)$. 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. (paper)