{"title":"关于复反射群的拟Steinberg性质","authors":"Ashish Mishra, Digjoy Paul, Pooja Singla","doi":"10.1007/s10468-023-10201-5","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>G</i> be a finite group and <i>p</i> be a prime number dividing the order of <i>G</i>. An irreducible character <i>χ</i> of <i>G</i> is called a quasi <i>p</i>-Steinberg character if <i>χ</i>(<i>g</i>) is nonzero for every <i>p</i>-regular element <i>g</i> in <i>G</i>. In this paper, we classify the quasi <i>p</i>-Steinberg characters of complex reflection groups <i>G</i>(<i>r</i>,<i>q</i>,<i>n</i>) and exceptional complex reflection groups. In particular, we obtain this classification for Weyl groups of type <i>B</i><sub><i>n</i></sub> and type <i>D</i><sub><i>n</i></sub>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"26 6","pages":"3101 - 3118"},"PeriodicalIF":0.6000,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Quasi Steinberg Characters of Complex Reflection Groups\",\"authors\":\"Ashish Mishra, Digjoy Paul, Pooja Singla\",\"doi\":\"10.1007/s10468-023-10201-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <i>G</i> be a finite group and <i>p</i> be a prime number dividing the order of <i>G</i>. An irreducible character <i>χ</i> of <i>G</i> is called a quasi <i>p</i>-Steinberg character if <i>χ</i>(<i>g</i>) is nonzero for every <i>p</i>-regular element <i>g</i> in <i>G</i>. In this paper, we classify the quasi <i>p</i>-Steinberg characters of complex reflection groups <i>G</i>(<i>r</i>,<i>q</i>,<i>n</i>) and exceptional complex reflection groups. In particular, we obtain this classification for Weyl groups of type <i>B</i><sub><i>n</i></sub> and type <i>D</i><sub><i>n</i></sub>.</p></div>\",\"PeriodicalId\":50825,\"journal\":{\"name\":\"Algebras and Representation Theory\",\"volume\":\"26 6\",\"pages\":\"3101 - 3118\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebras and Representation Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10468-023-10201-5\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-023-10201-5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
让 G 是有限群，p 是划分 G 的阶的素数。如果对于 G 中的每个 p 不规则元素 g，χ(g) 都非零，则 G 的不可还原字符 χ 称为准 p-斯泰恩伯格字符。特别是，我们获得了 Bn 型和 Dn 型韦尔群的这一分类。
On Quasi Steinberg Characters of Complex Reflection Groups
Let G be a finite group and p be a prime number dividing the order of G. An irreducible character χ of G is called a quasi p-Steinberg character if χ(g) is nonzero for every p-regular element g in G. In this paper, we classify the quasi p-Steinberg characters of complex reflection groups G(r,q,n) and exceptional complex reflection groups. In particular, we obtain this classification for Weyl groups of type Bn and type Dn.
期刊介绍：
Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups.
The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.
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