Abstract
A language is developed for ∂̄-cohomology, which is different from both the Dolbeault and the Čech descriptions, and involves only holomorphic objects. This language is then illustrated in certain cases of interest to representation theory. This makes possible a new geometric construction of the ladder representations for SU(2, p) and the non-holomorphic discrete series representations of SU(2, 1). The constructions are closely related to Penrose transforms.
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