To a pair of a Lie group and an open elliptic convex cone in its Lie algebra one associates a complex semigroup which permits an action of by biholomorphic mappings. In the case where is a vector space is a complex reductive group. In this paper we show that such semigroups are always Stein manifolds, that a biinvariant domain is Stein is and only if it is of the form , with convex, that each holomorphic function on extends to the smallest biinvariant Stein domain containing , and that biinvariant plurisubharmonic functions on correspond to invariant convex functions on .
À tout cône ouvert elliptique convexe dans l’algèbre de Lie d’un groupe de Lie on associe un semi-groupe complexe qui permet une action holomorphe de . Si est l’algèbre de Lie toute entière, le semi-groupe est un groupe complexe réductif. Dans cet article on montre que chaque semi-groupe est une variété de Stein, qu’un domaine biinvariant est de Stein si et seulement si où est convexe, que toute fonction holomorphe sur s’étend au plus petit domaine de Stein contenant , et que les fonctions biinvariantes plurisousharmoniques sur correspondent aux fonctions convexes sur .
@article{AIF_1998__48_1_149_0, author = {Neeb, Karl-Hermann}, title = {On the complex and convex geometry of {Ol'shanskii} semigroups}, journal = {Annales de l'Institut Fourier}, pages = {149--203}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {1}, year = {1998}, doi = {10.5802/aif.1614}, zbl = {0901.22003}, mrnumber = {99e:22013}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1614/} }
TY - JOUR AU - Neeb, Karl-Hermann TI - On the complex and convex geometry of Ol'shanskii semigroups JO - Annales de l'Institut Fourier PY - 1998 SP - 149 EP - 203 VL - 48 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1614/ DO - 10.5802/aif.1614 LA - en ID - AIF_1998__48_1_149_0 ER -
%0 Journal Article %A Neeb, Karl-Hermann %T On the complex and convex geometry of Ol'shanskii semigroups %J Annales de l'Institut Fourier %D 1998 %P 149-203 %V 48 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1614/ %R 10.5802/aif.1614 %G en %F AIF_1998__48_1_149_0
Neeb, Karl-Hermann. On the complex and convex geometry of Ol'shanskii semigroups. Annales de l'Institut Fourier, Volume 48 (1998) no. 1, pp. 149-203. doi : 10.5802/aif.1614. https://aif.centre-mersenne.org/articles/10.5802/aif.1614/
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