The $G$-stable pieces of the wonderful compactification
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- by Xuhua He PDF
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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.References
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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
- Received by editor(s): March 4, 2005
- Published electronically: February 21, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 3005-3024
- MSC (2000): Primary 20G15, 14L30
- DOI: https://doi.org/10.1090/S0002-9947-07-04158-X
- MathSciNet review: 2299444