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