{"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}
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.