$P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties
نویسندگان
چکیده
منابع مشابه
Dimensions of Affine Deligne-Lusztig Varieties in Affine Flag Varieties
Affine Deligne-Lusztig varieties are analogs of DeligneLusztig 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 DeligneLusztig 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...
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Let k be a finite field with q elements, and let k̄ be an algebraic closure of k. We consider the field L := k̄((ǫ)) and its subfield F := k((ǫ)). We write σ : x 7→ x for the Frobenius automorphism of k̄/k, and we also regard σ as an automorphism of L/F in the usual way, so that σ( ∑ anǫ ) = ∑ σ(an)ǫ . We write o for the valuation ring k̄[[ǫ]] of L. Let G be a split connected reductive group over k...
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This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.
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This paper concerns the dimensions of certain affine Deligne-Lusztig varieties, both in the affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the dimensions of the varieties Xμ(b) in the affine Grassmannian. We prove his conjecture for b in the split torus; we find that these varieties are equidimensional; and we reduce the general conjecture to the case of...
متن کاملThe Dimension of Some Affine Deligne-lusztig Varieties
We prove Rapoport’s dimension conjecture for affine Deligne-Lusztig varieties for GLh and superbasic b. From this case the general dimension formula for affine DeligneLusztig varieties for special maximal compact subgroups of split groups follows, as was shown in a recent paper by Görtz, Haines, Kottwitz, and Reuman.
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2015
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2254