It is known that the closure of an arbitrary -orbit on a flag manifold is expressed as a product of a closed -orbit and a Schubert cell ([M2], [Sp]). We already applied this fact to the duality of orbits on flag manifolds ([GM]). We refine here this result and give its new applications to the study of domains arising from the duality.
Simon GINDIKIN. Toshihiko MATSUKI. "A remark on Schubert cells and the duality of orbits on flag manifolds." J. Math. Soc. Japan 57 (1) 157 - 165, January, 2005. https://doi.org/10.2969/jmsj/1160745819