The 𝐺-stable pieces of the wonderful compactification

He, Xuhua

doi:10.1090/S0002-9947-07-04158-X

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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