Connected components of closed affine Deligne-Lusztig varieties

Eva Viehmann

doi:10.1007/s00208-007-0153-8

Connected components of closed affine Deligne-Lusztig varieties

Eva Viehmann

University of Bonn

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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.

Original language	English
Pages (from-to)	315-333
Number of pages	19
Journal	Mathematische Annalen
Volume	340
Issue number	2
DOIs	https://doi.org/10.1007/s00208-007-0153-8
State	Published - Feb 2008
Externally published	Yes

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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.",

author = "Eva Viehmann",

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AB - 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.

UR - https://www.scopus.com/pages/publications/38349098628

U2 - 10.1007/s00208-007-0153-8

DO - 10.1007/s00208-007-0153-8

M3 - Article

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VL - 340

SP - 315

EP - 333

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 2

ER -

Connected components of closed affine Deligne-Lusztig varieties

Abstract

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