Indefinite harmonic forms and gauge theory
A geometrical realization of the unitary highest weight representations of the conformal and the de Sitter groups (lying in the analytic continuation of the holomorphic discrete series) is given as the unitary quotient of an indecomposable representation using the indefinite harmonic forms [\textit{J. Rawnsley}, \textit{W. Schmid}, \textit{J. A. Wolf}, J. Funct. Anal. 51, 1-114 (1983; Zbl 0511.22005)]. The relation between these representations and the known massless, positive energy representations of SU(2,2) is established. It is demonstrated that this construction (after corresponding extension) allows to consider the twistor theory as a gauge field theory of SU(2,2). However such an approach is shown in the paper to be inapplicable to the gauge theory of the Dirac singletons based on the de Sitter group.
scientific article; zbMATH DE number 4077591
scientific article