Indefinite harmonic forms and gauge theory

Indecomposable representations have been extensively used in the construction of conformal and de Sitter gauge theories. It is thus noteworthy that certain unitary highest weight representations have been given a geometric realization as the unitary quotient of an indecomposable representation using indefinite harmonic forms [RSW]. We apply this construction toSU (2,2) and the de Sitter group. The relation is established between these representations and the massless, positive energy representations ofSU (2,2) obtained in the physics literature. We investigate the extent to which this construction allows twistors to be viewed as a gauge theory ofSU (2,2). For the de Sitter group, on which the gauge theory of singletons is based, we find that this construction is not directly applicable.