{"title":"超字符理论通过群行列式","authors":"Shawn T. Burkett","doi":"10.1216/rmj.2021.51.447","DOIUrl":null,"url":null,"abstract":"Ferdinand Georg Frobenius is generally considered the creator of character theory of finite groups. This achievement came from the study of the group determinant, which is the determinant of a matrix coming from the regular representation. In this paper, we generalize several of Frobenius' results about the group determinant and use them find a new formulation of supercharacter theory in terms of factorizations of the group determinant.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"55 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Supercharacter theory via the group determinant\",\"authors\":\"Shawn T. Burkett\",\"doi\":\"10.1216/rmj.2021.51.447\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Ferdinand Georg Frobenius is generally considered the creator of character theory of finite groups. This achievement came from the study of the group determinant, which is the determinant of a matrix coming from the regular representation. In this paper, we generalize several of Frobenius' results about the group determinant and use them find a new formulation of supercharacter theory in terms of factorizations of the group determinant.\",\"PeriodicalId\":275006,\"journal\":{\"name\":\"arXiv: Representation Theory\",\"volume\":\"55 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1216/rmj.2021.51.447\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1216/rmj.2021.51.447","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ferdinand Georg Frobenius is generally considered the creator of character theory of finite groups. This achievement came from the study of the group determinant, which is the determinant of a matrix coming from the regular representation. In this paper, we generalize several of Frobenius' results about the group determinant and use them find a new formulation of supercharacter theory in terms of factorizations of the group determinant.
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