Stein extensions of Riemann symmetric spaces and its generalization

Toshihiko Matsuki

Abstract: 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.

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