  Let H be a closed subgroup of a linear algebraic group G defined over a field
F. There is an equivalence of categories between the category of linear
finite-dimensional representations of H and the category of finite rank
G-homogeneous vectorbundles on G/H. In this short note we study this
correspondence for the sheaves of principal parts (=jetbundles) of homogeneous
linebundles on projective space in characteristic zero. We describe the
representation corresponding to the principal parts of a homogeneous linebundle
and as a corollary we obtain known formulas on the splitting type of the
principal parts on projective space in any dimension.
