Isometries of Hermitian symmetric spaces

1. Introduction
A Riemannian symmetric space M is called a
symmetric R-space if M is realized as an orbit of a linear
isotropy representation of a Riemannian symmetric space
of compact type.
Every Hermitian symmetric space M of compact type is
a symmetric R-space since M is realized as an adjoint
orbit of a compact semisimple Lie group.
3