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The $ G$-stable pieces of the wonderful compactification

Author(s): Xuhua He
Journal: Trans. Amer. Math. Soc. 359 (2007), 3005-3024.
MSC (2000): Primary 20G15, 14L30
Posted: February 21, 2007
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Abstract: Let $ G$ be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification $ \bar {G}$ of $ G$ into finite many $ G$-stable pieces, which was introduced by Lusztig. In this paper, we will investigate the closure of any $ G$-stable piece in $ \bar {G}$. We will show that the closure is a disjoint union of some $ G$-stable pieces, which was first conjectured by Lusztig. We will also prove the existence of cellular decomposition if the closure contains finitely many $ G$-orbits.

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Additional Information:

Xuhua He
Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
Address at time of publication: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794
Email: xuhua@mit.edu, hugo@math.mit.edu, hugo@math.sunysb.edu

DOI: 10.1090/S0002-9947-07-04158-X
PII: S 0002-9947(07)04158-X
Received by editor(s): March 4, 2005
Posted: February 21, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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