A Note on Principal Parts on Projective Space and Linear Representations

Details A Note on Principal Parts on Projective Space and Linear Representations A Note on Principal Parts on Projective Space and Linear Representations

2002-03-03

arxiv.org/abs/math/0203021v1

Mathematics

Algebraic Geometry

6 pages

Scientific paper

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.

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