{"title":"Stiefel-Whitney Classes for finite special linear groups of even rank","authors":"Neha Malik , Steven Spallone","doi":"10.1016/j.jalgebra.2025.03.009","DOIUrl":null,"url":null,"abstract":"<div><div>We compute the total Stiefel-Whitney Classes (SWCs) for orthogonal representations of special linear groups <span><math><mi>SL</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> when <em>n</em> and <em>q</em> are odd. These classes are expressed in terms of character values at diagonal elements of order 2. We give several consequences, and work out the 4th SWC explicitly, and the 8th SWC when the 4th vanishes.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"673 ","pages":"Pages 455-473"},"PeriodicalIF":0.8000,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002186932500119X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We compute the total Stiefel-Whitney Classes (SWCs) for orthogonal representations of special linear groups when n and q are odd. These classes are expressed in terms of character values at diagonal elements of order 2. We give several consequences, and work out the 4th SWC explicitly, and the 8th SWC when the 4th vanishes.
期刊介绍:
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.