Sui Chung Ng, HKU, Hong Kong

Rigidity of holomorphic mappings on flag domains on complex Grassmannians

Abstract

Let G be a complex simple Lie group and P be a parabolic subgroup. A flag domain on the rational homogeneous space (flag manifold) G/P is an open orbit of a real form G₀ of G. In this talk, we will look at certain cycle spaces of the SU(m, n)-type flag domains on complex Grassmannians. The cycles that we are interested in are some totally geodesic subgrassmannians. We are going to deduce from the structure of these cycle spaces some rigidity results of holomorphic mappings between Grassmannians. These include a local characterization of the automorphisms of the above flag domains which is analogous to the classical Alexander-Henkin-Tumanov theorem on irreducible bounded symmetric domains.