We characterize the nonemptiness and dimension problems for an affine Deligne–Lusztig variety in the affine flag variety in terms of galleries that are positively folded with respect to a chimney. If the parabolic subgroup associated to the Newton point of has rank 1, we then prove nonemptiness for a certain class of Iwahori–Weyl group elements by explicitly constructing such galleries.
Nous donnons une caractérisation des problèmes d’existence et de dimension pour une variété affine de Deligne–Lusztig dans la variété de drapeaux affine, en utilisant des galeries pliées positivement par rapport à une cheminée. Nous prouvons ensuite, en construisant explicitement telles galeries, que si le sous-groupe parabolique associé au point de Newton de a rang 1, les variétés sont non vides pour une certaine classe d’éléments du groupe d’Iwahori–Weyl.
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Keywords: Affine Deligne–Lusztig variety, positively folded gallery, chimney retraction.
Mot clés : Variété affine de Deligne–Lusztig, galeries pliées positivement, rétraction de cheminée.
Milićević, Elizabeth 1; Schwer, Petra 2; Thomas, Anne 3
CC-BY-ND 4.0
@article{AIF_2023__73_6_2469_0,
author = {Mili\'cevi\'c, Elizabeth and Schwer, Petra and Thomas, Anne},
title = {Affine {Deligne{\textendash}Lusztig} varieties and folded galleries governed by chimneys},
journal = {Annales de l'Institut Fourier},
pages = {2469--2541},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {73},
number = {6},
year = {2023},
doi = {10.5802/aif.3578},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3578/}
}
TY - JOUR AU - Milićević, Elizabeth AU - Schwer, Petra AU - Thomas, Anne TI - Affine Deligne–Lusztig varieties and folded galleries governed by chimneys JO - Annales de l'Institut Fourier PY - 2023 SP - 2469 EP - 2541 VL - 73 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3578/ DO - 10.5802/aif.3578 LA - en ID - AIF_2023__73_6_2469_0 ER -
%0 Journal Article %A Milićević, Elizabeth %A Schwer, Petra %A Thomas, Anne %T Affine Deligne–Lusztig varieties and folded galleries governed by chimneys %J Annales de l'Institut Fourier %D 2023 %P 2469-2541 %V 73 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3578/ %R 10.5802/aif.3578 %G en %F AIF_2023__73_6_2469_0
Milićević, Elizabeth; Schwer, Petra; Thomas, Anne. Affine Deligne–Lusztig varieties and folded galleries governed by chimneys. Annales de l'Institut Fourier, Volume 73 (2023) no. 6, pp. 2469-2541. doi : 10.5802/aif.3578. https://aif.centre-mersenne.org/articles/10.5802/aif.3578/
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