On univalence of equivariant Riemann domains over the complexification of a non-compact, Riemannian symmetric space

Let G/K be a non-compact, rank-one, Riemannian symmetric space and let G^C be the universal complexification of G. We prove that a holomorphically separable, G-equivariant Riemann domain over G^C / K^C is necessarily univalent, provided that G is not a covering of SL(2, R). As a consequence of the a...

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Bibliographic Details
Published in:arXiv.org 2006-12
Main Authors: Geatti, Laura, Iannuzzi, Andrea
Format: Article
Language:English
Subjects:
Domains
Invariants
Mathematical analysis
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Summary:Let G/K be a non-compact, rank-one, Riemannian symmetric space and let G^C be the universal complexification of G. We prove that a holomorphically separable, G-equivariant Riemann domain over G^C / K^C is necessarily univalent, provided that G is not a covering of SL(2, R). As a consequence of the above statement one obtains a univalence result for holomorphically separable, G x K -equivariant Riemann domains over G^C. Here G x K acts on G^C by left and right translations. The proof of such results involves a detailed study of the G-invariant complex geometry of the quotient G^C / K^C, including a complete classification of all its Stein G-invariant subdomains.
ISSN:2331-8422