The local orbit types of symmetric spaces under the actions of the isotropy subgroups
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.
scientific article; zbMATH DE number 1339070
scientific article