Classification of strict wonderful varieties

Bravi, Paolo; Cupit-Foutou, Stéphanie

Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 641-681.

D’après la conjecture de Luna, les variétés magnifiques peuvent être classifiées en termes d’objets combinatoires, les systèmes sphériques. Dans le présent article, nous prouvons cette conjecture dans le cas des variétés magnifiques dites strictes. Nous montrons, en particulier, que les variétés magnifiques strictes et primitives sont, pour la plupart, des variétés symétriques, des orbites nilpotentes sphériques ou des espaces modèles. Afin de faciliter la lecture de cet article, nous rappelons quelques faits connus sur ces variétés et, plus généralement, sur les variétés magnifiques.

In the setting of strict wonderful varieties we prove Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that primitive strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits and model spaces. To make the paper as self-contained as possible, we also gather some known results on these families and more generally on wonderful varieties.

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