The $G$-stable pieces of the wonderful compactification

• Autores: Xuhua He
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 7, 2007, págs. 3005-3024
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04158-x
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• Resumen

  • 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.