Invariants and matrix elements of the quantum group $U_q\left[gl\right(n,C\left)\right]$ revisited

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 . Here we provide an alternative evaluation utilising the R-matrix . 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. (paper)