Stein extensions of Riemann symmetric spaces and some generalization

Abstract

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.

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

Cited by in corpus (8)

• Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint
• The image of the heat kernel transform on Riemannian symmetric spaces of the noncompact type
• Fourier series on compact symmetric spaces
• Holomorphic Extension of Eigenfunctions
• Equivalence of domains arising from duality of orbits on flag manifolds III
• A refinement of the complex convexity theorem via symplectic techniques
• Crown theory for the upper halfplane
• Analysis on the crown domain