The Penrose transformation is constructed on general non-classical flag domains, and for large weights it gives isomorphisms between higher automorphic cohomology and automorphic forms on Hermitian symmetric domains.
Bott, Homogeneous vector bundles, Annals of Math
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Penrose transformation on flag domains
The Penrose transformation is constructed on general non-classical flag domains, and for large weights it gives isomorphisms between higher automorphic cohomology and automorphic forms on Hermitian symmetric domains.