A note on principal parts on projective space and linear representations

Abstract

Let H H be a closed subgroup of a linear algebraic group G G defined over a field of characteristic zero. There is an equivalence of categories between the category of linear finite-dimensional representations of H H , and the category of finite rank G G -homogeneous vector bundles on G / H G/H . In this paper we will study this correspondence for the sheaves of principal parts on projective space, and we describe the representation corresponding to the principal parts of a line bundle on projective space.