{"title":"The self-dual indecomposable modules in blocks with cyclic defect groups","authors":"Caroline Lassueur, John Murray","doi":"arxiv-2409.05562","DOIUrl":null,"url":null,"abstract":"Let $p$ be an odd prime and let $\\mathbf{B}$ be a $p$-block of a finite\ngroup, such that $\\mathbf{B}$ has cyclic defect groups. We describe the\nself-dual indecomposable $\\mathbf{B}$-modules and for each such module\ndetermine whether it is symplectic or orthogonal.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","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-2409.05562","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
Let $p$ be an odd prime and let $\mathbf{B}$ be a $p$-block of a finite
group, such that $\mathbf{B}$ has cyclic defect groups. We describe the
self-dual indecomposable $\mathbf{B}$-modules and for each such module
determine whether it is symplectic or orthogonal.