  The Schwinger oscillator operator representation of SU(3) is analysed with
particular reference to the problem of multiplicity of irreducible
representations. It is shown that with the use of an $Sp(2,R)$ unitary
representation commuting with the SU(3) representation, the infinity of
occurrences of each SU(3) irreducible representation can be handled in complete
detail. A natural `generating representation' for SU(3), containing each
irreducible representation exactly once, is identified within a subspace of the
Schwinger construction; and this is shown to be equivalent to an induced
representation of SU(3).
