The intersection of two real flag manifolds in a complex flag manifold, and the canonical form of a compact symmetric triad

Abstract

The necessary and sufficient conditions for the intersection of two real flag manifolds in a complex flag manifold to be discrete are stated including a previous known result. The discrete intersection of real flag manifolds is the orbit of a Weyl group, which is an antipodal set of a complex flag manifold. The triple of two real flag manifolds and a complex flag manifold as an ambient space is constructed from a compact symmetric triad. It is shown that the compact symmetric triad can be taken to be canonical.

arXiv comment29 pages