{"title":"Irreducible characters of the generalized symmetric group","authors":"Huimin Gao, Naihuan Jing","doi":"arxiv-2408.04921","DOIUrl":null,"url":null,"abstract":"The paper studies how to compute irreducible characters of the generalized\nsymmetric group $C_k\\wr{S}_n$ by iterative algorithms. After reproving the\nMurnaghan-Nakayama rule by vertex algebraic method, we formulate a new\niterative formula for characters of the generalized symmetric group. As\napplications, we find a numerical relation between the character values of\n$C_k\\wr S_n$ and modular characters of $S_{kn}$.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-09","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-2408.04921","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
The paper studies how to compute irreducible characters of the generalized
symmetric group $C_k\wr{S}_n$ by iterative algorithms. After reproving the
Murnaghan-Nakayama rule by vertex algebraic method, we formulate a new
iterative formula for characters of the generalized symmetric group. As
applications, we find a numerical relation between the character values of
$C_k\wr S_n$ and modular characters of $S_{kn}$.
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