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Wonderful varieties of type $D$


Authors: Paolo Bravi and Guido Pezzini
Journal: Represent. Theory 9 (2005), 578-637
MSC (2000): Primary 14L30; Secondary 14M17
DOI: https://doi.org/10.1090/S1088-4165-05-00260-8
Published electronically: November 18, 2005
MathSciNet review: 2183057
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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
MR Author ID: 683748
Email: bravi@math.unipd.it

Guido Pezzini
Affiliation: Dipartimento di Matematica, Università La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy
MR Author ID: 772887
Email: pezzini@mat.uniroma1.it

Received by editor(s): October 21, 2004
Received by editor(s) in revised form: August 2, 2005
Published electronically: November 18, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.