Uniformity of holomorphic vector bundles on infinite-dimensional flag manifolds

Abstract

Let V be a localizing infinite-dimensional complex Banach space. Let X be a flag manifold of finite flags either offinite codimensionalclosed linear subspaces of V or of finite dimensional linear subspaces of V. Let E be a holomorphicvector bundle on X with finite rank. Here we prove that E is uniform, i.e. that for any two lines D, R in the samesystem of lines on X the vector bundles Evert D and Evert R have the same splitting type.