{"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":49887,"journal":{"name":"Manuscripta Mathematica","volume":"6 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Manuscripta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01566-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.