In this paper we investigate invariant domains in Xi+, a distinguished G-invariant, Stein domain in the complexification of an irreducible Hermitian symmetric space G/K. The domain Xi+, recently introduced by Krötz and Opdam, contains the crown domain and it is maximal with respect to properness of the G-action. In the tube case, it also contains S+, an invariant Stein domain arising from the compactly causal structure of a symmetric orbit in the boundary of Xi. We prove that the envelope of holomorphy of an invariant domain in Xi+, which is contained neither in Xi nor in S+, is univalent and coincides with Xi+. This fact, together with known results concerning and S+, proves the univalence of the envelope of holomorphy of an arbitrary invariant domain in Xi+ and completes the classification of invariant Stein domains therein

Geatti, L., Iannuzzi, A. (2016). Invariant envelopes of holomorphy in the complexification of a hermitian symmetric space. ANNALES DE L'INSTITUT FOURIER, 66(1), 143-174 [10.5802/aif.3008].

Invariant envelopes of holomorphy in the complexification of a hermitian symmetric space

Geatti, Laura;Iannuzzi, Andrea
2016-01-01

Abstract

In this paper we investigate invariant domains in Xi+, a distinguished G-invariant, Stein domain in the complexification of an irreducible Hermitian symmetric space G/K. The domain Xi+, recently introduced by Krötz and Opdam, contains the crown domain and it is maximal with respect to properness of the G-action. In the tube case, it also contains S+, an invariant Stein domain arising from the compactly causal structure of a symmetric orbit in the boundary of Xi. We prove that the envelope of holomorphy of an invariant domain in Xi+, which is contained neither in Xi nor in S+, is univalent and coincides with Xi+. This fact, together with known results concerning and S+, proves the univalence of the envelope of holomorphy of an arbitrary invariant domain in Xi+ and completes the classification of invariant Stein domains therein
2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Crown domain, Hermitian symmetric space, envelope of holomorphy
http://aif.cedram.org/cedram-bin/article/AIF_2016__66_1_143_0.pdf
Geatti, L., Iannuzzi, A. (2016). Invariant envelopes of holomorphy in the complexification of a hermitian symmetric space. ANNALES DE L'INSTITUT FOURIER, 66(1), 143-174 [10.5802/aif.3008].
Geatti, L; Iannuzzi, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/200130
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