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A Note on Principal Parts on Projective Space and Linear Representations

Helge Øystein Maakestad
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Abstract

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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Helge Øystein Maakestad. 2002-03-03. A Note on Principal Parts on Projective Space and Linear Representations. https://arxiv.org/abs/math/0203021

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