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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Flag varieties as equivariant compactifications of $ \mathbb{G}_{a}^{n}$


Author: Ivan V. Arzhantsev
Journal: Proc. Amer. Math. Soc. 139 (2011), 783-786
MSC (2010): Primary 14M15; Secondary 14L30
Published electronically: October 22, 2010
MathSciNet review: 2745631
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Abstract: Let $ G$ be a semisimple affine algebraic group and $ P$ a parabolic subgroup of $ G$. We classify all flag varieties $ G/P$ which admit an action of the commutative unipotent group $ \mathbb{G}_{a}^{n}$ with an open orbit.


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Additional Information

Ivan V. Arzhantsev
Affiliation: Department of Higher Algebra, Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory 1, GSP-1, Moscow, 119991, Russia
Email: arjantse@mccme.ru

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10723-2
PII: S 0002-9939(2010)10723-2
Keywords: Semisimple groups, parabolic subgroups, flag varieties, automorphisms
Received by editor(s): March 14, 2010
Published electronically: October 22, 2010
Additional Notes: The author was supported by RFBR Grants 09-01-00648-a, 09-01-90416-Ukr-f-a, and the Deligne 2004 Balzan Prize in Mathematics.
Communicated by: Harm Derksen
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.