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A note on principal parts on projective space and linear representations
Author(s):
Helge
Maakestad
Journal:
Proc. Amer. Math. Soc.
133
(2005),
349-355.
MSC (2000):
Primary 14L30, 20C15
Posted:
September 2, 2004
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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:
10.1090/S0002-9939-04-07453-2
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
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