Wonderful varieties of type 𝐷

Bravi, Paolo; Pezzini, Guido

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

Wonderful varieties of type $D$
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by Paolo Bravi and Guido Pezzini

Represent. Theory 9 (2005), 578-637

DOI: https://doi.org/10.1090/S1088-4165-05-00260-8

Published electronically: November 18, 2005

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Abstract:

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

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