
Journal of Lie Theory 13 (2003), No. 2, 565572 Copyright Heldermann Verlag 2003 Stein Extensions of Riemann Symmetric Spaces and some Generalization Toshihiko Matsuki Faculty of Integrated Human Studies, Kyoto University, Kyoto 6068501, Japan We give a proof that the AkhiezerGindikin 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 AkhiezerGindikin domain D is contained in all cycle spaces. [ Fulltextpdf (181 KB)] for subscribers only. 