We investigate the joint action of two real forms of a semi-simple complex Lie group by left and right multiplication. After analyzing the orbit structure, we study the CR structure of closed orbits. The main results are an explicit formula of the Levi form of closed orbits and the determination of the Levi cone of generic orbits. Finally, we apply these results to prove -completeness of certain invariant domains in .
@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/
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