We investigate the CR geometry of the orbits of a real form of a complex semisimple Lie group in a complex flag manifold . We are mainly concerned with finite type and holomorphic nondegeneracy conditions, canonical -equivariant and Mostow fibrations, and topological properties of the orbits.
@article{ASNSP_2010_5_9_1_69_0, author = {Altomani, Andrea and Medori, Costantino and Nacinovich, Mauro}, title = {Orbits of real forms in complex flag manifolds}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {69--109}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 9}, number = {1}, year = {2010}, mrnumber = {2668874}, zbl = {1198.53051}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2010_5_9_1_69_0/} }
TY - JOUR AU - Altomani, Andrea AU - Medori, Costantino AU - Nacinovich, Mauro TI - Orbits of real forms in complex flag manifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 69 EP - 109 VL - 9 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2010_5_9_1_69_0/ LA - en ID - ASNSP_2010_5_9_1_69_0 ER -
%0 Journal Article %A Altomani, Andrea %A Medori, Costantino %A Nacinovich, Mauro %T Orbits of real forms in complex flag manifolds %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 69-109 %V 9 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2010_5_9_1_69_0/ %G en %F ASNSP_2010_5_9_1_69_0
Altomani, Andrea; Medori, Costantino; Nacinovich, Mauro. Orbits of real forms in complex flag manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 9 (2010) no. 1, pp. 69-109. http://archive.numdam.org/item/ASNSP_2010_5_9_1_69_0/
[1] Algorithims for representation theory of real groups, J. Inst. Math. Jussieu 8 (2009), 209–256. | MR
and ,[2] The CR structure of minimal orbits in complex flag manifolds, J. Lie Theory 16 (2006), 483–530. | MR | Zbl
, and ,[3] On the topology of minimal orbits in complex flag manifolds, Tohoku Math. J. 60 (2008), 403–422. | MR | Zbl
, and ,[4] On root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka City Univ. 13 (1962), 1–34. | MR
,[5] “Real Submanifolds in Complex Space and their Mappings”, Vol. 47, Princeton University Press, Princeton, NJ, 1999. | MR
, and ,[6] On index number and topology of flag manifolds, Differential Geom. Appl. 15 (2001), 81–90. | MR | Zbl
, and ,[7] A geometric characterization of points of type on real submanifolds of , J. Differential Geom. 12 (1977), 171–182. | MR | Zbl
and ,[8] “Éléments de mathématique”, Hermann, Paris, 1975, Fasc. XXXVIII: Groupes et algèbres de Lie. Chapitre VII: Sous-algèbres de Cartan, éléments réguliers. Chapitre VIII: Algèbres de Lie semi-simples déployées, Actualités Scientifiques et Industrielles, No. 1364. | MR | Zbl
,[9] Orbit duality for flag manifolds, Manuscripta Math. 109 (2002), 233–261. | MR | Zbl
and ,[10] Schubert cells and representation theory, Invent. Math. 137 (1999), 461–539. | MR | Zbl
and ,[11] Locally homogeneous finitely nondegenerate CR-manifolds, Math. Res. Lett. 14 (2007), 893–922. | MR | Zbl
,[12] “Cycle Spaces of Flag Domains. A Complex Geometric Viewpoint”, Progress in Mathematics, Vol. 245, Birkhäuser Boston Inc., Boston, MA, 2006. | MR | Zbl
, and ,[13] Systems of roots and topology of complex flag manifolds, Geom. Dedicata 71 (1998), 299–308. | MR | Zbl
,[14] “Differential Geometry, Lie Groups, and Symmetric Spaces”, Pure and Applied Mathematics, Vol. 80, Academic Press, New York, 1978. | MR | Zbl
,[15] “Linear Algebraic Groups”, n. 21, Springer-Verlag, New York Graduate Texts in Mathematics, 1975. | MR
,[16] “Lie Groups Beyond an Introduction”, second ed., Progress in Mathematics, Vol. 140, Birkhäuser Boston Inc., Boston, MA, 2002. | MR | Zbl
,[17] Closure relations for orbits on affine symmetric spaces under the action of parabolic subgroups. Intersections of associated orbits, Hiroshima Math. J. 18 (1988), 59–67. | MR | Zbl
,[18] Levi-Tanaka algebras and homogeneous CR manifolds, Compositio Math. 109 (1997), 195–250. | MR | Zbl
and ,[19] Classification of semisimple Levi-Tanaka algebras, Ann. Mat. Pura Appl. 174 (1998), 285–349. | MR | Zbl
and ,[20] Complete nondegenerate locally standard CR manifolds, Math. Ann. 317 (2000), 509–526. | MR | Zbl
and ,[21] Algebras of infinitesimal CR automorphisms, J. Algebra 287 (2005), 234–274. | MR | Zbl
and ,[22] On covariant fiberings of Klein spaces, Amer. J. Math. 77 (1955), 247–278. | MR | Zbl
,[23] Covariant fiberings of Klein spaces. II, Amer. J. Math. 84 (1962), 466–474. | MR | Zbl
,[24] Two-number of symmetric -spaces, Nagoya Math. J. 115 (1989), 43–46. | MR | Zbl
,[25] Minimal imbeddings of -spaces, J. Differential Geom. 2 (1968), 203–215. | MR | Zbl
and ,[26] Irreducible characters of semisimple Lie groups. IV. Character-multiplicity duality, Duke Math. J. 49 (1982), 943–1073. | MR | Zbl
,[27] The fundamental group of a real flag manifold, Indag. Mat. 9 (1998), 141–153. | MR | Zbl
,[28] The action of a real semisimple group on a complex flag manifold. I. Orbit structure and holomorphic arc components, Bull. Amer. Math. Soc. 75 (1969), 1121–1237. | MR | Zbl
,