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Mathematische Annalen

, Volume 340, Issue 2, pp 315–333 | Cite as

Connected components of closed affine Deligne–Lusztig varieties

  • Eva ViehmannEmail author
Article

Abstract

We determine the set of connected components of closed affine Deligne–Lusztig varieties for special maximal compact subgroups of split connected reductive groups. We show that there is a transitive group action on this set. Thus such an affine Deligne–Lusztig variety has isolated points if and only if its dimension is 0. We also obtain a description of the set of these varieties that are zero-dimensional.

Keywords

Simple Root Dynkin Diagram Borel Subgroup Unipotent Radical Levi Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Refererences

  1. 1.
    Görtz U., Haines Th.J., Kottwitz R.E. and Reuman D.C. (2006). Dimensions of some affine Deligne–Lusztig varieties. Ann. Sci. École Norm. Sup. 39: 467–511 zbMATHGoogle Scholar
  2. 2.
    Kottwitz R.E. (1985). Isocrystals with additional structure. Comp. Math. 56: 201–220 zbMATHMathSciNetGoogle Scholar
  3. 3.
    Kottwitz R.E. (1997). Isocrystals with additional structure II. Comp. Math. 109: 255–339 zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kottwitz R.E. (2003). On the Hodge–Newton decomposition for split groups. IMRN 26: 1433–1447 CrossRefMathSciNetGoogle Scholar
  5. 5.
    Kottwitz R.E. and Rapoport M. (2003). On the existence of F-crystals. Comment. Math. Helv. 78: 153–184 zbMATHMathSciNetGoogle Scholar
  6. 6.
    Mantovan, E., Viehmann, E.: On the Hodge–Newton filtration for p-divisible \({\mathcal{O}}\) -modules (in preparation)Google Scholar
  7. 7.
    Mierendorff, E.: On affine Deligne–Lusztig varieties for GL n. Dissertation, Bonn (2005) http://www.hss.ulb.uni-bonn.de/diss_online/math_nat_fak/2005/mierendorff_eva/
  8. 8.
    Rapoport M. (2000). A positivity property of the Satake isomorphism. Manuscripta Math. 101(2): 153–166 zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Viehmann E. (2006). The dimension of some affine Deligne–Lusztig varieties. Ann. Sci. École Norm. Sup. 39: 513–526 zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany

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