HOMOGENEOUS VECTOR-BUNDLES AND KOSZUL ALGEBRAS

Let G be a reductive algebraic group defined over an algebraically clo sed field of characteristic zero and let P be a parabolic subgroup of G. We consider the category of homogeneous vector bundles over the fla g variety G/P. This category is equivalent to a category of representa tions of a certain infinite quiver with relations by a generalisation of a result in [BK]. We prove that both categories are Koszul precisel y when the unipotent radical P-u of P is abelian.