{"title":"The Frobenius Characteristic of Character Polynomials","authors":"Amritanshu Prasad","doi":"10.1007/s41745-022-00327-8","DOIUrl":null,"url":null,"abstract":"<div><p>Polynomials in an infinite sequence of variables can be evaluated as class functions of symmetric groups on <span>\\(n\\)</span> letters across all <span>\\(n\\)</span>. When they represent characters of families of representations, they are called character polynomials. This article is an introduction to the theory of character polynomials and their Frobenius characteristics. As an application, some generating functions describing the restriction of a polynomial representation of <span>\\(GL_n\\)</span> to <span>\\(S_n\\)</span> are obtained.</p></div>","PeriodicalId":675,"journal":{"name":"Journal of the Indian Institute of Science","volume":"102 3","pages":"947 - 959"},"PeriodicalIF":1.8000,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s41745-022-00327-8.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indian Institute of Science","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s41745-022-00327-8","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 1
Abstract
Polynomials in an infinite sequence of variables can be evaluated as class functions of symmetric groups on \(n\) letters across all \(n\). When they represent characters of families of representations, they are called character polynomials. This article is an introduction to the theory of character polynomials and their Frobenius characteristics. As an application, some generating functions describing the restriction of a polynomial representation of \(GL_n\) to \(S_n\) are obtained.
期刊介绍：
Started in 1914 as the second scientific journal to be published from India, the Journal of the Indian Institute of Science became a multidisciplinary reviews journal covering all disciplines of science, engineering and technology in 2007. Since then each issue is devoted to a specific topic of contemporary research interest and guest-edited by eminent researchers. Authors selected by the Guest Editor(s) and/or the Editorial Board are invited to submit their review articles; each issue is expected to serve as a state-of-the-art review of a topic from multiple viewpoints.
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