Journal of Lie Theory 13 (2003), No. 2, 565--572
Copyright Heldermann Verlag 2003
Stein Extensions of Riemann Symmetric Spaces and some Generalization
Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-8501, Japan
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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