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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Wonderful varieties of type $D$
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by Paolo Bravi and Guido Pezzini PDF
Represent. Theory 9 (2005), 578-637 Request permission


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:
  • Guido Pezzini
  • Affiliation: Dipartimento di Matematica, Università La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy
  • MR Author ID: 772887
  • Email:
  • Received by editor(s): October 21, 2004
  • Received by editor(s) in revised form: August 2, 2005
  • Published electronically: November 18, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 9 (2005), 578-637
  • MSC (2000): Primary 14L30; Secondary 14M17
  • DOI:
  • MathSciNet review: 2183057