Invariants, Projection Operators and SU(N)×SU(N) Irreducible Schwinger Bosons

We exploit SU(N) Schwinger bosons to construct and analyze the coupled irreducible repre-sentations of SU(N) × SU(N) in terms of the invariant group. The corresponding projec-tion operators are constructed in terms of the invariant group generators. We also construct SU(N) × 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. PACS: 02.20.-a, 02.20.Sv, 03.65.-w, 31.10.+z