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COMPACT ORBITS OF PARABOLIC SUBGROUPS.
- Source :
-
Nagoya Mathematical Journal . Sep2022, Vol. 247, p615-623. 9p. - Publication Year :
- 2022
-
Abstract
- 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 $\mu _{\mathfrak p}$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00277630
- Volume :
- 247
- Database :
- Academic Search Index
- Journal :
- Nagoya Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 159054005
- Full Text :
- https://doi.org/10.1017/nmj.2021.14