Journal of Lie Theory

no. 2
Stein Extensions of Riemann Symmetric Spaces and some Generalization
Journal of Lie Theory, Volume 13 (2003) no. 2, pp. 565-572
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.
DOI: 10.5802/jolt.320
Classification: 22E46, 22E15
Keywords: Akhiezer-Gindikin domain, Iwasawa domain, semisimple Lie group 
@article{JOLT_2003_13_2_a14,
     author = {T. 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},
     doi = {10.5802/jolt.320},
     zbl = {1042.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.320/}
}
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%J Journal of Lie Theory
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T. Matsuki. Stein Extensions of Riemann Symmetric Spaces and some Generalization. Journal of Lie Theory, Volume 13 (2003) no. 2, pp. 565-572. doi: 10.5802/jolt.320

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