The $G$-stable pieces of the wonderful compactification

Details The $G$-stable pieces of the wonderful compactification The $G$-stable pieces of the wonderful compactification

2004-12-15

arxiv.org/abs/math/0412302v3

Mathematics

Representation Theory

22 pages. Some corrections. Final version

Scientific paper

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 were 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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