IJPAM: Volume 16, No. 2 (2004)

UNIFORMITY OF PRINCIPAL BUNDLES
ON INFINITE-DIMENSIONAL FLAG MANIFOLDS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


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 $G$ be a connected reduced algebraic group and $E$ a principal $G$-bundle bundle on $X$. 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 $G$-bundless $E\vert D$ and $E\vert R$ are isomorphic.

Received: June 11, 2004

AMS Subject Classification: 32K05, 32L05

Key Words and Phrases: flag manifold, infinite-dimensional flag manifold, holomorphic vector bundle, uniform vector bundle, splitting type

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 2