Affine Deligne–Lusztig varieties and folded galleries governed by chimneys
Annales de l'Institut Fourier, Volume 73 (2023) no. 6, pp. 2469-2541.

We characterize the nonemptiness and dimension problems for an affine Deligne–Lusztig variety X x (b) 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 b has rank 1, we then prove nonemptiness for a certain class of Iwahori–Weyl group elements x by explicitly constructing such galleries.

Nous donnons une caractérisation des problèmes d’existence et de dimension pour une variété affine de Deligne–Lusztig X x (b) 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 b a rang 1, les variétés X x (b) sont non vides pour une certaine classe d’éléments x du groupe d’Iwahori–Weyl.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3578
Classification: 20G25, 11G25, 20F55, 20E42, 14L05
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

1 Department of Mathematics & Statistics Haverford College 370 Lancaster Avenue Haverford, PA (USA)
2 Department of Mathematics Universitaetsplatz 2 Otto-von-Guericke University of Magdeburg (Germany)
3 School of Mathematics & Statistics Carslaw Building F07 University of Sydney NSW 2006 (Australia)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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