The intersection of two real forms in Hermitian symmetric spaces of compact type II

Abstract

We minutely describe the intersection of two real forms in a non-irreducible Hermitian symmetric space $M$ of compact type. In the case where $M$ is irreducible we have already done it in our previous paper. In this paper we reduce the description of the intersection of two real forms to that in some special cases. This reduction is based on the information of the group of all isometries obtained by Takeuchi. We can describe the intersection in the special cases and in all cases. In particular we obtain the intersection number of two real forms in a Hermitian symmetric space of compact type.