The -stable pieces of the wonderful compactification

Author:
Xuhua He

Journal:
Trans. Amer. Math. Soc. **359** (2007), 3005-3024

MSC (2000):
Primary 20G15, 14L30

Published electronically:
February 21, 2007

MathSciNet review:
2299444

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification of into finite many -stable pieces, which was introduced by Lusztig. In this paper, we will investigate the closure of any -stable piece in . We will show that the closure is a disjoint union of some -stable pieces, which was first conjectured by Lusztig. We will also prove the existence of cellular decomposition if the closure contains finitely many -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:
http://dx.doi.org/10.1090/S0002-9947-07-04158-X

Received by editor(s):
March 4, 2005

Published electronically:
February 21, 2007

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.