Geodesic
The CR Structure of Minimal Orbits in Complex Flag Manifolds
Andrea Altomani1 ; Costantino Medori2 ; Mauro Nacinovich1
1Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00185 Roma, Italy
2Dip. di Matematica, Università di Parma, Parco Area delle Scienze 53/A, 43100 Parma, Italy
Journal of Lie Theory, Tome 16 (2006) no. 3, pp. 483-530

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 32V05, 14M15, 17B20, 22E15, 32M10
Mots-clés : Complex flag manifold, homogeneousCR manifold, minimal orbit of a real form, parabolic CR algebra

Andrea Altomani  1   ; Costantino Medori  2   ; Mauro Nacinovich  1

1 Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00185 Roma, Italy
2 Dip. di Matematica, Università di Parma, Parco Area delle Scienze 53/A, 43100 Parma, Italy 
Andrea Altomani; Costantino Medori; Mauro Nacinovich. The CR Structure of Minimal Orbits in Complex Flag Manifolds. Journal of Lie Theory, Tome 16 (2006) no. 3, pp. 483-530. http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a4/
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     author = {Andrea Altomani and Costantino Medori and Mauro Nacinovich},
     title = {The {CR} {Structure} of {Minimal} {Orbits} in {Complex} {Flag} {Manifolds}},
     journal = {Journal of Lie Theory},
     pages = {483--530},
     year = {2006},
     volume = {16},
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     url = {http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a4/}
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