2014/03/19 by Huckleberry, Alan
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1403.4993
A flag domain D is an open orbit of a real form G0 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 G0 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.