Symmetry properties of SU3 vector coupling coefficients

A presentation of the problem of calculating the vector coupling coefficients for $SU3 \supset SU2 \otimes U1$ is made, in the spirit of traditional treatments of SU2 coupling. The coefficients are defined as the overlap matrix element between product states and a coupled state with good SU3 quantum numbers. A technique for resolution of the outer degeneracy problem, based upon actions of the infinitesimal generators of SU3 is developed, which automatically produces vector coupling coefficients with symmetries under exchange of state labels which parallel the familiar symmetries of the SU2 case. An algorithm for efficient computation of these coefficients is outlined, for which an ANSI C code is available.