Geodesic
Dimensions of affine Deligne-Lusztig varieties in affine flag varieties.
Documenta mathematica, Tome 15 (2010), pp. 1009-1028
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Affine Deligne-Lusztig varieties are analogs of Deligne-Lusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper [5] by Haines, Kottwitz, Reuman, and the first named author, about the question which affine Deligne-Lusztig varieties (for a split group and a basic σ-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a classical group and the chosen basic σ-conjugacy class is the class of b=1, we also prove the dimension formula predicted in op. cit. in almost all cases.
DOI : 10.4171/dm/322
Classification : 20F55, 20G25
Mots-clés : affine Deligne-Lusztig varieties 
@article{10_4171_dm_322,
     author = {Ulrich G\"ortz and Xuhua He},
     title = {Dimensions of affine {Deligne-Lusztig} varieties in affine flag varieties.},
     journal = {Documenta mathematica},
     pages = {1009--1028},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/322},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/322/}
}
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Ulrich Görtz; Xuhua He. Dimensions of affine Deligne-Lusztig varieties in affine flag varieties.. Documenta mathematica, Tome 15 (2010), pp. 1009-1028. doi: 10.4171/dm/322

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