Uniform non-homogeneous vector bundles: A counterexample to the conjecture of Drézet and Ballico-Ellia

We construct a rank-9 uniform non-homogeneous vector bundle on ${\mathbb{P}}^5$. This yields the first counterexample to the longstanding open conjecture that every uniform vector bundle of rank $r<2n$ on ${\mathbb{P}}^n$ is homogeneous.