Uniform vector bundles on rational homogeneous spaces

Let X be a rational homogeneous space. It is well known that X can be
embedded in a projective space so that it is covered by lines. A
vector bundle on X is said to be uniform if its restriction to any
line is the same. A uniform vector bundle E on X induces a morphism
from the variety of lines through a point x ? X into a suitable flag
variety. In this talk I will explain how we can recover geometric
information about E from this morphism. In particular, I will discuss
splitting criteria for uniform vector bundles on rational homogeneous
spaces.
This is a joint work with Nicolas Puignau.