Wonderful varieties of type 𝐷

Abstract

Let G G be a connected semisimple group over C \mathbb C , whose simple components have type A \mathsf A or D \mathsf D . We prove that wonderful G G -varieties are classified by means of combinatorial objects called spherical systems. This is a generalization of a known result of Luna for groups of type A \mathsf A ; thanks to another result of Luna, this implies also the classification of all spherical G G -varieties for the groups G G we are considering. For these G G we also prove the smoothness of the embedding of Demazure.