Stein extensions of Riemann symmetric spaces and some generalization

Details Stein extensions of Riemann symmetric spaces and some generalization Stein extensions of Riemann symmetric spaces and some generalization

2002-08-23

arxiv.org/abs/math/0208175v2

J. of Lie Theory 13(2003), 563-570

Mathematics

Representation Theory

8 pages, modified for a new version of a cited preprint

Scientific paper

It was proved by Huckleberry that the Akhiezer-Gindikin domain is included in the ``Iwasawa domain'' using complex analysis. But we can see that we need no complex analysis to prove it. In this paper, we generalize the notions of the Akhiezer-Gindikin domain and the Iwasawa domain for two associated symmetric subgroups in real Lie groups and prove the inclusion. Moreover, by the symmetry of two associated symmetric subgroups, we also give a direct proof of the known fact that the Akhiezer-Gindikin domain is included in all cycle spaces.

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