Uniform (d+1)-bundle over the Grassmannian G(d,n)

Abstract

This paper is dedicated to the classification of uniform vector bundles of rank $d+1$ over the Grassmannian $G(d,n)$ ($d\le n-d$) over an algebraically closed field in characteristic $0$. Specifically, we show that all uniform vector bundles with rank $d+1$ over $G(d,n)$ are homogeneous.