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We resolve the SU(3) outer multiplicity problem by defining all possible$SU(3)\otimes SU(3)$ invariant operators in terms of SU(3) Schwinger bosons. Weshow that the elementary invariant operators relevant to the outer multiplicityproblem form SO(4,2) algebra. Further, they enable us to construct a family ofoperators any one of which can be used to distinguish repeating representationspresent in the reduction of the direct product of two SU(3) irreduciblerepresentations.

Resolution of SU(3) Outer Multiplicity Problem and the $SU(3)\otimes SU(3)$ Invariant Group $SO(4,2)$