{"title":"THE VERTICES OF THE COMPONENTS OF THE PERMUTATION MODULE INDUCED FROM PARABOLIC GROUPS","authors":"Lars Pforte","doi":"10.18910/70821","DOIUrl":null,"url":null,"abstract":"We consider the permutation module kP↑GLn(p f ), where P is a parabolic group in the general linear group GLn(p f ) and k is an algebraically closed field of prime characteristic p. The vertices of the components of these modules have been calculated in [9] by Tinberg, who studied these modules for all groups with split BN-pairs in characteristic p. In this paper we show that the idea of suitability is strong enough to find all p-groups that are vertex of some component of kP↑GLn(p f ). Furthermore using a result of Burry and Carlson we show that all components have a different vertex.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.18910/70821","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We consider the permutation module kP↑GLn(p f ), where P is a parabolic group in the general linear group GLn(p f ) and k is an algebraically closed field of prime characteristic p. The vertices of the components of these modules have been calculated in [9] by Tinberg, who studied these modules for all groups with split BN-pairs in characteristic p. In this paper we show that the idea of suitability is strong enough to find all p-groups that are vertex of some component of kP↑GLn(p f ). Furthermore using a result of Burry and Carlson we show that all components have a different vertex.
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