A note on principal parts on projective space and linear representations
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- by Helge Maakestad PDF
- Proc. Amer. Math. Soc. 133 (2005), 349-355 Request permission
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.References
- Dmitri N. Akhiezer, Lie group actions in complex analysis, Aspects of Mathematics, E27, Friedr. Vieweg & Sohn, Braunschweig, 1995. MR 1334091, DOI 10.1007/978-3-322-80267-5
- Armand Borel, Linear algebraic groups, 2nd ed., Graduate Texts in Mathematics, vol. 126, Springer-Verlag, New York, 1991. MR 1102012, DOI 10.1007/978-1-4612-0941-6
- Fernando Cukierman, Determinant of complexes and higher Hessians, Math. Ann. 307 (1997), no. 2, 225–251. MR 1428872, DOI 10.1007/s002080050032
- Jens Carsten Jantzen, Representations of algebraic groups, Pure and Applied Mathematics, vol. 131, Academic Press, Inc., Boston, MA, 1987. MR 899071
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
- H. Maakestad, Modules of principal parts on the projective line, preprint math.AG/0111149.
- David Perkinson, Principal parts of line bundles on toric varieties, Compositio Math. 104 (1996), no. 1, 27–39. MR 1420708
- Ragni Piene and Gianni Sacchiero, Duality for rational normal scrolls, Comm. Algebra 12 (1984), no. 9-10, 1041–1066. MR 738534, DOI 10.1080/00927878408823038
- Sandra Di Rocco and Andrew J. Sommese, Line bundles for which a projectivized jet bundle is a product, Proc. Amer. Math. Soc. 129 (2001), no. 6, 1659–1663. MR 1814094, DOI 10.1090/S0002-9939-00-05875-5
- Andrew John Sommese, Compact complex manifolds possessing a line bundle with a trivial jet bundle, Abh. Math. Sem. Univ. Hamburg 47 (1978), 79–91. MR 499332, DOI 10.1007/BF02941353
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
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2093054