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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The $G$-stable pieces of the wonderful compactification
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by Xuhua He PDF
Trans. Amer. Math. Soc. 359 (2007), 3005-3024 Request permission

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
  • 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