Uniformity of holomorphic vector bundles on infinite-dimensional flag manifolds

Bull. Korean Math. Soc. 2003 Vol. 40, No. 1, 85-89 Published online March 1, 2003

E. Ballico University of Trento

Abstract : Let $V$ be a localizing infinite-dimensional complex Banach space. Let $X$ be a flag manifold of finite flags either of finite codimensional closed linear subspaces of $V$ or of finite dimensional linear subspaces of $V$. Let $E$ be a holomorphic vector bundle on $X$ with finite rank. Here we prove that $E$ is uniform, i.e. that for any two lines $D$, $R$ in the same system of lines on $X$ the vector bundles $E\vert D$ and $E\vert R$ have the same splitting type.

Keywords : flag manifold, infinite-dimensional flag manifold, holomorphic vector bundle, uniform vector bundle, splitting type