1Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-8501, Japan 2We give a proof that the Akhiezer-Gindikin domain D is contained in the "Iwasawa domain". A proof of this containment was given by Huckleberry using complex analysis. By contrast, we need no complex analysis in this paper. In fact, we prove a theorem generalized for two associated symmetric subgroups in real Lie groups. Moreover, by the symmetry of two associated symmetric subgroups, we can also give a direct proof of the known fact that the Akhiezer-Gindikin domain D is contained in all cycle spaces. 3[
Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 565-572
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Toshihiko Matsuki. Stein Extensions of Riemann Symmetric Spaces and some Generalization. Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 565-572. http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a14/
@article{JOLT_2003_13_2_a14,
author = {Toshihiko Matsuki},
title = {Stein {Extensions} of {Riemann} {Symmetric} {Spaces} and some {Generalization}},
journal = {Journal of Lie Theory},
pages = {565--572},
year = {2003},
volume = {13},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a14/}
}
TY - JOUR
AU - Toshihiko Matsuki
TI - Stein Extensions of Riemann Symmetric Spaces and some Generalization
JO - Journal of Lie Theory
PY - 2003
SP - 565
EP - 572
VL - 13
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a14/
ID - JOLT_2003_13_2_a14
ER -
%0 Journal Article
%A Toshihiko Matsuki
%T Stein Extensions of Riemann Symmetric Spaces and some Generalization
%J Journal of Lie Theory
%D 2003
%P 565-572
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a14/
%F JOLT_2003_13_2_a14
We give a proof that the Akhiezer-Gindikin domain D is contained in the "Iwasawa domain". A proof of this containment was given by Huckleberry using complex analysis. By contrast, we need no complex analysis in this paper. In fact, we prove a theorem generalized for two associated symmetric subgroups in real Lie groups. Moreover, by the symmetry of two associated symmetric subgroups, we can also give a direct proof of the known fact that the Akhiezer-Gindikin domain D is contained in all cycle spaces.
