A remark on Schubert cells and the duality of orbits on flag manifolds

Abstract

It is known that the closure of an arbitrary K_{\bc}-orbit on a flag manifold is expressed as a product of a closed K_{\bc}-orbit and a Schubert cell (\cite{M2}, \cite{Sp}). We already applied this fact to the duality of orbits on flag manifolds (\cite {GM}). We refine here this result and give its new applications to the study of domains arising from the duality.