The CR structure of minimal orbits in complex flag manifolds

Let bG be a complex semisimple Lie group, Q a parabolic subgroup and G a real form of bG. The flag manifold bG/Q decomposes into finitely many G-orbits; among them there is exactly one orbit of minimal dimension, which is compact. We study these minimal orbits from the point of view of CR geometry. In particular we characterize those minimal orbits that are of finite type and satisfy various nondegeneracy conditions, compute their fundamental group and describe the space of their global CR functions. Our main tool are parabolic CR algebras, which give an infinitesimal description of the CR structure of minimal orbits.