We investigate the joint action of two real forms of a semi-simple complex Lie group
@article{ASNSP_2009_5_8_3_509_0, author = {Miebach, Christian}, title = {Geometry of invariant domains in complex semi-simple {Lie} groups}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {509--541}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 8}, number = {3}, year = {2009}, mrnumber = {2581425}, zbl = {1184.22006}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2009_5_8_3_509_0/} }
TY - JOUR AU - Miebach, Christian TI - Geometry of invariant domains in complex semi-simple Lie groups JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 509 EP - 541 VL - 8 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2009_5_8_3_509_0/ LA - en ID - ASNSP_2009_5_8_3_509_0 ER -
%0 Journal Article %A Miebach, Christian %T Geometry of invariant domains in complex semi-simple Lie groups %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 509-541 %V 8 %N 3 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2009_5_8_3_509_0/ %G en %F ASNSP_2009_5_8_3_509_0
Miebach, Christian. Geometry of invariant domains in complex semi-simple Lie groups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 3, pp. 509-541. http://www.numdam.org/item/ASNSP_2009_5_8_3_509_0/
[1] Théorème de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193–259. | EuDML | Numdam | MR | Zbl
and ,[2] Plurisubharmonic functions and Kählerian metrics on complexification of symmetric spaces, Indag. Math. (N.S.) 3 (1992), 365–375. | MR | Zbl
and ,[3] “Real Submanifolds in Complex Space and their Mappings”, Princeton Mathematical Series, Vol. 47, Princeton University Press, Princeton, NJ, 1999. | MR | Zbl
, and ,[4] “CR Manifolds and the Tangential Cauchy-Riemann complex”, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1991. | MR | Zbl
,[5] Invariant analytic domains in complex semisimple groups, Transform. Groups 1 (1996), 279–305. | MR | Zbl
,[6] “Theory of Lie Groups. I”, Princeton University Press, Princeton, N. J., 1946 [Eighth Printing, 1970]. | MR | Zbl
,[7] “Complex Analytic and Algebraic Geometry”, available at http://www-fourier.ujf-grenoble.fr/ demailly/books.html.
,[8] Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960), 94–123. | EuDML | MR | Zbl
and ,[9] Cohomologically complete and pseudoconvex domains, Comment. Math. Helv. 55 (1980), 413–426. | EuDML | MR | Zbl
and ,[10] Geometry of biinvariant subsets of complex semisimple Lie groups, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 26 (1998), 329–356. | EuDML | Numdam | MR | Zbl
and ,[11] Spherical functions of a real semisimple Lie group. A method of reduction to the complex case, J. Funct. Anal. 30 (1978), 106–146. | MR | Zbl
,[12] “Lie Semigroups and their Applications”, Lecture Notes in Mathematics, Vol. 1552, Springer-Verlag, Berlin, 1993. | MR | Zbl
and ,[13] Cartan decomposition of the moment map, Math. Ann. 337 (2007), 197–232. | MR | Zbl
and ,[14] “Conjugacy Classes in Semisimple Algebraic Groups”, Mathematical Surveys and Monographs, Vol. 43, American Mathematical Society, Providence, RI, 1995. | MR | Zbl
,[15] “Vorlesungen über Torische Varietäten”, Konstanzer Schriften in Mathematik und Informatik, Nr. 130, Fassung vom Herbst 2001.
,[16] “Foundations of Differential Geometry. Vol I”, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. | MR | Zbl
and ,[17] “Lie Groups Beyond an Introduction”, second ed., Progress in Mathematics, Vol. 140, Birkhäuser Boston Inc., Boston, MA, 2002. | MR | Zbl
,[18] Sur la transformation de Fourier-Laurent dans un groupe analytique complexe réductif, Ann. Inst. Fourier (Grenoble) 28 (1978), 115–138. | EuDML | Numdam | MR | Zbl
,[19] Double coset decompositions of reductive Lie groups arising from two involutions, J. Algebra 197 (1997), 49–91. | MR | Zbl
,[20] Classification of two involutions on compact semisimple Lie groups and root systems, J. Lie Theory 12 (2002), 41–68. | EuDML | MR | Zbl
,[21] Geometry of invariant domains in complex semi-simple Lie groups, Dissertation, Bochum, 2007.
,[22] Invariant convex sets and functions in Lie algebras, Semigroup Forum 53 (1996), 230–261. | EuDML | MR | Zbl
,[23] On the complex and convex geometry of Ol’shanskiĭsemigroups, Ann. Inst. Fourier (Grenoble) 48 (1998), 149–203. | EuDML | Numdam | MR | Zbl
,[24] “Holomorphy and Convexity in Lie Theory”, de Gruyter Expositions in Mathematics, Vol. 28, Walter de Gruyter & Co., Berlin, 2000. | MR | Zbl
,[25] On the existence of slices for actions of non-compact Lie groups, Ann. of Math. (2) 73 (1961), 295–323. | MR | Zbl
,[26] “Endomorphisms of Linear Algebraic Groups”, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968. | MR | Zbl
,[27] “Lie Groups and Lie Algebras, III”, Encyclopaedia of Mathematical Sciences, Vol. 41, Springer-Verlag, Berlin, 1994. | Zbl
(ed.),