  In a previous paper the generator matrix elements and (dual) vector reduced
Wigner coefficients (RWCs) were evaluated via the polynomial identities
satisfied by a certain matrix constructed from the $R$-matrix $R$ and its
twisted counterpart $R^T=T\circ R$. Here we provide an alternative evaluation
utilising the $R$-matrix $\tilde{R} = (R^T)^{-1}$. This provides a new direct
derivation of the vector RWCs obtained indirectly in earlier work via a
symmetry relation. This approach has the advantage that it generalises to the
Lie superalgebra case, which will be investigated elsewhere.
