列维分组中的牛顿层

Pub Date : 2024-06-04 DOI:10.1007/s00229-024-01566-y
Felix Schremmer
{"title":"列维分组中的牛顿层","authors":"Felix Schremmer","doi":"10.1007/s00229-024-01566-y","DOIUrl":null,"url":null,"abstract":"<p>Certain Iwahori double cosets in the loop group of a reductive group, known under the names of <i>P</i>-alcoves or <span>\\((J,w,\\delta )\\)</span>-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Newton strata in Levi subgroups\",\"authors\":\"Felix Schremmer\",\"doi\":\"10.1007/s00229-024-01566-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Certain Iwahori double cosets in the loop group of a reductive group, known under the names of <i>P</i>-alcoves or <span>\\\\((J,w,\\\\delta )\\\\)</span>-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00229-024-01566-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01566-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

还原群环群中的某些岩崛双oset以P-弧或((J,w,\delta )\)-弧的名称而闻名,它们在仿射德利涅-鲁斯提格(Deligne-Lusztig)变体的研究中发挥着重要作用。对于这样的岩崛双余弦,它的牛顿分层与列维子群中岩崛双余弦的牛顿分层相关。我们进一步研究了这种关系,特别是提供了出现的牛顿分层之间的双射关系。作为应用,我们证明了 Dong-Gyu Lim 的一个猜想,给出了基本仿射 Deligne-Lusztig 变体的非emptiness 准则。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
分享
查看原文
Newton strata in Levi subgroups

Certain Iwahori double cosets in the loop group of a reductive group, known under the names of P-alcoves or \((J,w,\delta )\)-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信