Formulas for the dimensions of some affine Deligne-Lusztig Varieties

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dc.creatorReuman, Daniel C.
dc.date2003-03-12
dc.date.accessioned2026-07-07T04:55:58Z
dc.date.available2026-07-07T04:55:58Z
dc.descriptionRapoport and Kottwitz defined the affine Deligne-Lusztig varieties $X_{\tilde{w}}^P(bσ)$ of a quasisplit connected reductive group $G$ over $F = \mathbb{F}_q((t))$ for a parahoric subgroup $P$. They asked which pairs $(b, \tilde{w})$ give non-empty varieties, and in these cases what dimensions do these varieties have. This paper answers these questions for $P=I$ an Iwahori subgroup, in the cases $b=1$, $G=SL_2$, $SL_3$, $Sp_4$. This information is used to get a formula for the dimensions of the $X_{\tilde{w}}^K(σ)$ (all shown to be non-empty by Rapoport and Kottwitz) for the above $G$ that supports a general conjecture of Rapoport. Here $K$ is a special maximal compact subgroup.
dc.description16 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/math/0303146
dc.identifierhttp://arxiv.org/abs/math/0303146
dc.identifierMichigan Math. J. 52 (2004), 435-451
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66768
dc.subjectRepresentation Theory
dc.subject20G25
dc.titleFormulas for the dimensions of some affine Deligne-Lusztig Varieties
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