A combinatorial study of affine Deligne-Lusztig varieties

dc.contributor.advisorHe, Xuhuaen_US
dc.contributor.advisorAdams, Jeffreyen_US
dc.contributor.authorSadhukhan, Arghyaen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2023-10-06T05:47:34Z
dc.date.available2023-10-06T05:47:34Z
dc.date.issued2023en_US
dc.description.abstractWe consider affine Deligne-Lusztig varieties $X_w(b)$ and certain unions $X(\mu,b)$ in the affine flag variety of a connected reductive group. They were first introduced by Rapoport to facilitate the study of mod-$p$ reduction of Shimura varieties and moduli spaces of shtukas. We improve upon certain existing results in the study of affine Deligne-Lusztig varieties by weakening the hypothesis to prove them. Such results include a description of generic Newton points in Iwahori double cosets in the loop group of a split reductive group, covering relations in the associated Iwahori-Weyl group, and a dimension formula for $X(\mu,b)$ in the case of a quasi-split group. As an application of the work on generic Newton point formula, we obtain a description of the dimension for $X(\mu,b)$ associated with the maximal element $b$ in its natural range, under a mild hypothesis on $\mu$ but no further restrictions on the group.en_US
dc.identifierhttps://doi.org/10.13016/dspace/o9cu-wheb
dc.identifier.urihttp://hdl.handle.net/1903/30783
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledAffine Deligne-Lusztig varietyen_US
dc.subject.pquncontrolledAffine Weyl groupen_US
dc.subject.pquncontrolledQuantum Bruhat graphen_US
dc.subject.pquncontrolledShimura varietyen_US
dc.titleA combinatorial study of affine Deligne-Lusztig varietiesen_US
dc.typeDissertationen_US

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