The local orbit types of symmetric spaces under the actions of the isotropy subgroups
type: Item
instance of: scholarly article
title: The local orbit types of symmetric spaces under the actions of the isotropy subgroups
zbMATH Open document ID: 0941.53035
DOI: 10.1016/S0926-2245(99)00023-6
author: Hiroshi Tamaru
published in: Differential Geometry and its Applications
publication date: 1999-09-22T00:00:00Z
review text: Let \(M=G/K\) be a compact semi-simple symmetric space, where \(G\) is the identity component of the isometry group. The author investigates the set of the local orbit types of the action of \(K\) on \(M\) and provides a nice way to determine the set of local orbit types. He defines the corresponding subalgegra of a closed subsystem in the restricted root system and shows that every isotropy subalgebra at a point in the maximal torus is the corresponding subalgebra of a certain closed system. He then proves that it is sufficient, for determining the set of local orbit types, to consider the set of closed subsystems obtained from subdiagrams of the extended Dynkin diagram.
reviewed by: Bang-Yen Chen
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 57S15
zbMATH DE Number: 1339070
zbMATH Keywords: Dynkin diagram
zbMATH Keywords: polars
zbMATH Keywords: isotropy subgroup
zbMATH Keywords: local orbit type
MaRDI profile type: Publication
Wikidata QID: Q115337416
cites work: Q3941610
cites work: Totally geodesic submanifolds of symmetric spaces. II
cites work: Semisimple subalgebras of semisimple Lie algebras
cites work: Q3897665
cites work: Differentiable actions of compact connected classical groups. II
cites work: Q4024281
cites work: The involutions of compact symmetric spaces. II
cites work: The involutions of compact symmetric spaces. III
cites work: Q3698971
cites work: Q4539664
cites work: Shape operators of orbits of isotropy subgroups in Riemannian symmetric spaces of the compact type
cites work: Homogeneous spaces defined by Lie group automorphisms. II
description: scientific article; zbMATH DE number 1339070