STEIN EXTENSIONS OF RIEMANN SYMMETRIC SPACES AND DUALITIES OF ORBITS ON FLAG MANIFOLDS

SIMON GINDIKIN TOSHIHIKO MATSUKI

Abstract. It is known that K_{ℂ}-orbits S and G_{ℝ}-orbits S′ on a complex flag manifold are in one-to-one correspondence by the condition that S ∩ S′ is nonempty and compact. We may replace K_{ℂ} by some conjugate xK_{ℂ}x^{−1} so that the correspondence is preserved. We will show that this replacement is related to the domain introduced by Akhiezer and Gindikin.