Reduction of a Class of O(4, 2) Representations with Respect to SO(4, 1) and SO(3, 2)

A complete classification of representations of SO(4, 2) with infinitesimal generators SAB, characterized by the representation relation {SAB, SAC} = −2agBC, and their extension by parity have been determined. The possible values of a are a = 1 − S2, S = 0, 12, 1, 32, 2, ⋯. These representations have then been reduced according to the two chains SO(4,2)⊃SO(4,1)⊃SO(4)⊃SO(3) and SO(4,2)⊃SO(3,2)⊃SO(3)⊗SO(2). The equivalence of these representations with the oscillator representations is established.