Cycle Connectivity and Automorphism Groups of Flag Domains

A flag domain $D$ is an open orbit of a real form $G_0$ in a flag manifold $Z=G\mathrm{/}P$ of its complexification. If $D$ is holomorphically convex, then, since it is a product of a Hermitian symmetric space of bounded type and a compact flag manifold, $Aut(D)$ is easily described. If $D$ is not holomorphically convex, then in our previous work (American J. Math, 136, Nr.2 (2013) 291-310 (arXiv: 1003.5974)) it was shown that $Aut(D)$ is a Lie group whose connected component at the identity agrees with $G_0$ except possibly in situations which arise in Onishchik’s list of flag manifolds where $Aut(Z{)}^0$ is larger than $G$. These exceptions are handled in detail here. In addition substantially simpler proofs of some of our previous work are given.