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Wonderful varieties of type $ D$

Author(s): Paolo Bravi; Guido Pezzini
Journal: Represent. Theory 9 (2005), 578-637.
MSC (2000): Primary 14L30; Secondary 14M17
Posted: 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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Additional Information:

Paolo Bravi
Affiliation: Dipartimento di Matematica, Università La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy
Address at time of publication: Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via G. Belzoni 7, 35131 Padova, Italy
Email: bravi@math.unipd.it

Guido Pezzini
Affiliation: Dipartimento di Matematica, Università La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy
Email: pezzini@mat.uniroma1.it

DOI: 10.1090/S1088-4165-05-00260-8
PII: S 1088-4165(05)00260-8
Received by editor(s): October 21, 2004
Received by editor(s) in revised form: August 2, 2005
Posted: November 18, 2005
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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