{"title":"经典韦尔群中的高等列字符和根枚举","authors":"Ron M. Adin , Pál Hegedüs , Yuval Roichman","doi":"10.1016/j.jalgebra.2024.10.013","DOIUrl":null,"url":null,"abstract":"<div><div>We prove that, for any integer <em>k</em>, the <em>k</em>-th root enumerator in the classical Weyl group of type <em>D</em> is a proper character. The proof uses higher Lie characters of type <em>B</em>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"664 ","pages":"Pages 26-72"},"PeriodicalIF":0.8000,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Higher Lie characters and root enumeration in classical Weyl groups\",\"authors\":\"Ron M. Adin , Pál Hegedüs , Yuval Roichman\",\"doi\":\"10.1016/j.jalgebra.2024.10.013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We prove that, for any integer <em>k</em>, the <em>k</em>-th root enumerator in the classical Weyl group of type <em>D</em> is a proper character. The proof uses higher Lie characters of type <em>B</em>.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"664 \",\"pages\":\"Pages 26-72\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-02-15\",\"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/S0021869324005556\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/10/22 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324005556","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/10/22 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们证明，对于任意整数 k，D 型经典韦尔群中的 k-th 根列举符是一个合适的字符。证明使用的是 B 型的高等李字符。
Higher Lie characters and root enumeration in classical Weyl groups
We prove that, for any integer k, the k-th root enumerator in the classical Weyl group of type D is a proper character. The proof uses higher Lie characters of type B.
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.
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