{"title":"Stiefel–Whitney classes of representations of SL(2, 𝑞)","authors":"Neha Malik, S. Spallone","doi":"10.1515/jgth-2022-0164","DOIUrl":null,"url":null,"abstract":"Abstract We describe the Stiefel–Whitney classes (SWCs) of orthogonal representations 𝜋 of the finite special linear groups G = SL ( 2 , F q ) G=\\operatorname{SL}(2,\\mathbb{F}_{q}) , in terms of character values of 𝜋. From this calculation, we can answer interesting questions about SWCs of 𝜋. For instance, we determine the subalgebra of H * ( G , Z / 2 Z ) H^{*}(G,\\mathbb{Z}/2\\mathbb{Z}) generated by the SWCs of orthogonal 𝜋, and we also determine which 𝜋 have non-trivial mod 2 Euler class.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":"26 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Group Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2022-0164","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract We describe the Stiefel–Whitney classes (SWCs) of orthogonal representations 𝜋 of the finite special linear groups G = SL ( 2 , F q ) G=\operatorname{SL}(2,\mathbb{F}_{q}) , in terms of character values of 𝜋. From this calculation, we can answer interesting questions about SWCs of 𝜋. For instance, we determine the subalgebra of H * ( G , Z / 2 Z ) H^{*}(G,\mathbb{Z}/2\mathbb{Z}) generated by the SWCs of orthogonal 𝜋, and we also determine which 𝜋 have non-trivial mod 2 Euler class.
期刊介绍:
The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.
Topics:
Group Theory-
Representation Theory of Groups-
Computational Aspects of Group Theory-
Combinatorics and Graph Theory-
Algebra and Number Theory