We carry out a detailed study of \Xi^+, a distinguished G-invariant Stein domain in the complexification of an irreducible Hermitian symmetric space G/K . The domain\Xi^+ contains the crown domain \Xi and is naturally diffeomorphic to the anti-holomorphic tangent bundle of G/K . The unipotent parametrization of \Xi^+ introduced in Krötz and Opdam (GAFA Geom Funct Anal 18:1326–1421, 2008) and Krötz (Invent Math 172:277–288, 2008) suggests that \Xi^+ also admits the structure of a twisted bundle G ×_K N^+, with fiber a nilpotent cone N^+ . Here we give a complete proof of this fact and use it to describe the G-orbit structure of \Xi^+ via the K-orbit structure of N^+. In the tube case, we also single out a Stein, G-invariant domain contained in \Xi^+ \setminus \Xi which is relevant in the classification of envelopes of holomorphy of invariant subdomains of \Xi^+.
Geatti, L., & Iannuzzi, A. (2014). Orbit structure of a distinguished Stein invariant domain in the complexification of a Hermitian symmetric space. MATHEMATISCHE ZEITSCHRIFT, 278(3-4), 769-793.
Tipologia: | Articolo su rivista |
Citazione: | Geatti, L., & Iannuzzi, A. (2014). Orbit structure of a distinguished Stein invariant domain in the complexification of a Hermitian symmetric space. MATHEMATISCHE ZEITSCHRIFT, 278(3-4), 769-793. |
URL: | http://link.springer.com/article/10.1007/s00209-014-1333-3 |
IF: | Con Impact Factor ISI |
Lingua: | English |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria |
Revisione (peer review): | Esperti anonimi |
Tipo: | Articolo |
Rilevanza: | Rilevanza internazionale |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00209-014-1333-3 |
Stato di pubblicazione: | Pubblicato |
Data di pubblicazione: | 2014 |
Titolo: | Orbit structure of a distinguished Stein invariant domain in the complexification of a Hermitian symmetric space |
Autori: | |
Autori: | Geatti, L; Iannuzzi, A |
Appare nelle tipologie: | 01 - Articolo su rivista |
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