Studying affine Deligne Lusztig varieties via folded galleries in buildings

Appears in collection : Algebraic Combinatorics in Representation Theory / Combinatoire algébrique en théorie des représentations

We present a new approach to affine Deligne Lusztig varieties which allows us to study the so called "non-basic" case in a type free manner. The central idea is to translate the question of non-emptiness and the computation of the dimensions of these varieties into geometric questions in the Bruhat-Tits building. All boils down to understand existence of certain positively folded galleries in affine Coxeter complexes. To do so, we explicitly construct such galleries and use, among other techniques, the root operators introduced by Gaussent and Littelmann to manipulate them.

Information about the video

Date of recording 01/09/2016
Date of publication 13/09/2016
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19042303
Cite this video Schwer, Petra (01/09/2016). Studying affine Deligne Lusztig varieties via folded galleries in buildings. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19042303
URL https://dx.doi.org/10.24350/CIRM.V.19042303

Domain(s)

Bibliography

Elizabeth Milicevic, Petra Schwer, Anne Thomas - Dimensions of affine Deligne-Lusztig varieties: a new approach via labeled folded alcove walks and root operators - 2015 - http://arxiv.org/abs/1504.07076