Resumen de The $G$-stable pieces of the wonderful compactification

Xuhua He

• Let G be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification of 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 . 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 -orbits.