{"title":"Some remarks about the faithfulness of the Burau representation of Artin--Tits groups","authors":"Asilata Bapat, Hoel Queffelec","doi":"arxiv-2409.00144","DOIUrl":null,"url":null,"abstract":"We discuss the extension of the faithfulness question for the Burau\nrepresentation of braid groups to the case of Artin--Tits groups. We prove that\nthe Burau representation is not faithful in affine type $\\tilde{A_3}$, and not\nfaithful over several finite rings in type $D_4$, using an algorithmic approach\nbased on categorical methods that generalize Bigelow's curve strategy outside\nof type $A$.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"7 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.00144","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We discuss the extension of the faithfulness question for the Burau
representation of braid groups to the case of Artin--Tits groups. We prove that
the Burau representation is not faithful in affine type $\tilde{A_3}$, and not
faithful over several finite rings in type $D_4$, using an algorithmic approach
based on categorical methods that generalize Bigelow's curve strategy outside
of type $A$.
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