COMPACT ORBITS OF PARABOLIC SUBGROUPS
| Autor: | Leonardo Biliotti, Oluwagbenga Windare |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Nagoya Mathematical Journal. 247:615-623 |
| ISSN: | 2152-6842 0027-7630 |
| DOI: | 10.1017/nmj.2021.14 |
| Popis: | We study the action of a real reductive group G on a real submanifold X of a Kähler manifold Z. We suppose that the action of a compact connected Lie group U with Lie algebra $\mathfrak {u}$ extends holomorphically to an action of the complexified group $U^{\mathbb {C}}$ and that the U-action on Z is Hamiltonian. If $G\subset U^{\mathbb {C}}$ is compatible, there exists a gradient map $\mu _{\mathfrak p}:X \longrightarrow \mathfrak p$ where $\mathfrak g=\mathfrak k \oplus \mathfrak p$ is a Cartan decomposition of $\mathfrak g$ . In this paper, we describe compact orbits of parabolic subgroups of G in terms of the gradient map $\mu _{\mathfrak p}$ . |
| Databáze: | OpenAIRE |
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