Let G be a connected semisimple group over C, whose simple components have type A or 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 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.
Wonderful varieties of type D / Bravi, Paolo; Pezzini, Guido. - In: REPRESENTATION THEORY. - ISSN 1088-4165. - 9:(2005), pp. 578-636. [10.1090/S1088-4165-05-00260-8]
Wonderful varieties of type D
BRAVI, Paolo;PEZZINI, Guido
2005
Abstract
Let G be a connected semisimple group over C, whose simple components have type A or 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 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.| File | Dimensione | Formato | |
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