A combinatorial study of affine Deligne-Lusztig varieties
dc.contributor.advisor | He, Xuhua | en_US |
dc.contributor.advisor | Adams, Jeffrey | en_US |
dc.contributor.author | Sadhukhan, Arghya | en_US |
dc.contributor.department | Mathematics | en_US |
dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
dc.date.accessioned | 2023-10-06T05:47:34Z | |
dc.date.available | 2023-10-06T05:47:34Z | |
dc.date.issued | 2023 | en_US |
dc.description.abstract | We 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.identifier | https://doi.org/10.13016/dspace/o9cu-wheb | |
dc.identifier.uri | http://hdl.handle.net/1903/30783 | |
dc.language.iso | en | en_US |
dc.subject.pqcontrolled | Mathematics | en_US |
dc.subject.pquncontrolled | Affine Deligne-Lusztig variety | en_US |
dc.subject.pquncontrolled | Affine Weyl group | en_US |
dc.subject.pquncontrolled | Quantum Bruhat graph | en_US |
dc.subject.pquncontrolled | Shimura variety | en_US |
dc.title | A combinatorial study of affine Deligne-Lusztig varieties | en_US |
dc.type | Dissertation | en_US |
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