Cycle Connectivity and Automorphism Groups of Flag Domains

Abstract

A flag domain $D$ is an open orbit of a real form $G_0$ in a flag manifold $Z=G/P$ 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.

To appear in Birkhäuser Progress Reports "Current Developments and Retrospectives in Lie Theory