Journal of Lie Theory 16 (2006), No. 3, 483--530
Copyright Heldermann Verlag 2006
The CR Structure of Minimal Orbits in Complex Flag Manifolds
Andrea Altomani
Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00185 Roma, Italy
altomani@mat.uniroma2.it
Costantino Medori
Dip. di Matematica, Università di Parma, Parco Area delle Scienze 53/A, 43100 Parma, Italy
costantino.medori@unipr.it
Mauro Nacinovich
Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00185 Roma, Italy
nacinovi@mat.uniroma2.it
Let G-hat be a complex semisimple Lie group, Q a parabolic subgroup and G a real form of G-hat. The flag manifold G-hat / 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.
Keywords: Complex flag manifold, homogeneousCR manifold, minimal orbit of a real form, parabolic CR algebra.
MSC: 32V05; 14M15, 17B20, 22E15, 32M10
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