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 | References | Similar Articles | Additional Information

Abstract: Let be a closed subgroup of a linear algebraic group defined over a field of characteristic zero. There is an equivalence of categories between the category of linear finite-dimensional representations of , and the category of finite rank -homogeneous vector bundles on . 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