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

Abstract: 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.