Journal of Lie Theory

no. 3
The CR Structure of Minimal Orbits in Complex Flag Manifolds
Journal of Lie Theory, Volume 16 (2006) no. 3, pp. 483-530
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.
DOI: 10.5802/jolt.421
Classification: 32V05, 14M15, 17B20, 22E15, 32M10
Keywords: Complex flag manifold, homogeneousCR manifold, minimal orbit of a real form, parabolic CR algebra 
@article{JOLT_2006_16_3_a4,
     author = {A. Altomani and C. Medori and M. Nacinovich},
     title = {The {CR} {Structure} of {Minimal} {Orbits} in {Complex} {Flag} {Manifolds}},
     journal = {Journal of Lie Theory},
     pages = {483--530},
     year = {2006},
     volume = {16},
     number = {3},
     doi = {10.5802/jolt.421},
     zbl = {1120.32023},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.421/}
}
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A. Altomani; C. Medori; M. Nacinovich. The CR Structure of Minimal Orbits in Complex Flag Manifolds. Journal of Lie Theory, Volume 16 (2006) no. 3, pp. 483-530. doi: 10.5802/jolt.421

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