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Proceedings of the American Mathematical Society

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A note on principal parts on projective space and linear representations


Author: Helge Maakestad
Journal: Proc. Amer. Math. Soc. 133 (2005), 349-355
MSC (2000): Primary 14L30, 20C15
DOI: https://doi.org/10.1090/S0002-9939-04-07453-2
Published electronically: September 2, 2004
MathSciNet review: 2093054
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Abstract: Let $H$ be a closed subgroup of a linear algebraic group $G$defined over a field of characteristic zero. There is an equivalence of categories between the category of linear finite-dimensional representations of $H$, and the category of finite rank $G$-homogeneous vector bundles on $G/H$. 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.


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Additional Information

Helge Maakestad
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel
Address at time of publication: Department of Mathematics, KTH, 10044 Stockholm, Sweden
Email: makesth@macs.biu.ac.il

DOI: https://doi.org/10.1090/S0002-9939-04-07453-2
Keywords: Homogeneous spaces, homogeneous vector bundles, principal parts, linear representations, splitting type
Received by editor(s): May 16, 2002
Received by editor(s) in revised form: July 7, 2003
Published electronically: September 2, 2004
Additional Notes: This work was partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center “Group Theoretic Methods in the Study of Algebraic Varieties” of the Israel Science Foundation and the EAGER Foundation (EU network, HPRN-CT-2000-00099)
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society