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We exploit SU(N) Schwinger bosons to construct and analyze the coupledirreducible representations of $SU(N) \times SU(N)$ in terms of the invariantgroup. The corresponding projection operators are constructed in terms of theinvariant group generators. We also construct $SU(N) \times SU(N)$ irreducibleSchwinger bosons which directly create these coupled irreducible states. TheSU(N) Clebsch Gordan coefficients are computed as the matrix elements of theprojection operators.

Invariants, Projection Operators and $SU(N)\times SU(N)$ Irreducible Schwinger Bosons