Nondegenerate CR geometries with simple models

I will talk about nondegenerate CR geometries with Levi-Tanaka algebra such that its Tanaka prolongation is simple Lie algebra. These belong to the class of parabolic geometries, for which there is explicit solution of the equivalence problem. This allows to characterize the fundamental invariants of these CR geometries in terms of Lie algebra valued cohomologies that can be computed using Kostant's version of Bott-Borel-Weyl theorem. For majority of these CR geometries, the relevant cohomologies vanish and imply that such a CR geometries are unique.