Wonderful varieties of type 𝐷

Bravi, Paolo; Pezzini, Guido

doi:10.1090/S1088-4165-05-00260-8

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ISSN 1088-4165

Wonderful varieties of type

Authors: Paolo Bravi and Guido Pezzini
Journal: Represent. Theory 9 (2005), 578-637
MSC (2000): Primary 14L30; Secondary 14M17
Posted: November 18, 2005
MathSciNet review: 2183057
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Abstract: Let be a connected semisimple group over $\mathbb{C}$ , whose simple components have type $\mathsf A$ or $\mathsf D$ . We prove that wonderful -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 $\mathsf A$ ; thanks to another result of Luna, this implies also the classification of all spherical -varieties for the groups we are considering. For these we also prove the smoothness of the embedding of Demazure.

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