Kottwitz-Rapoport conjecture on unions 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...
متن کاملDimensions of Some Affine Deligne-lusztig Varieties
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...
متن کاملAffine Deligne-lusztig Varieties in Affine Flag Varieties
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.
متن کاملOn a Conjecture of Kottwitz and Rapoport
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all split and quasi-split (connected) reductive groups. These results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.
متن کاملOn Some Stratifications of Affine Deligne-lusztig Varieties for Sl3
Let L := k̄((ǫ)), where k is a finite field with q elements and ǫ is an indeterminate, and let σ be the Frobenius automorphism. Let G be a split connected reductive group over the fixed field of σ in L, and let I be the Iwahori subgroup of G(L) associated to a given Borel subgroup of G. Let f W be the extended affine Weyl group of G. Given x ∈ f W and b ∈ G(L), we have some subgroup of G(L) that...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2016
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2305