有限群的射影(或自旋)表示。二

Tatsuya Tsurii, Satoe Yamanaka, Itsumi Mikami, Takeshi Hirai
{"title":"有限群的射影(或自旋)表示。二","authors":"Tatsuya Tsurii, Satoe Yamanaka, Itsumi Mikami, Takeshi Hirai","doi":"arxiv-2408.03486","DOIUrl":null,"url":null,"abstract":"In the previous paper, we proposed a practical method of constructing\nexplicitly representation groups $R(G)$ for finite groups $G$, and apply it to\ncertain typical finite groups $G$ with Schur multiplier $M(G)$ containing prime\nnumber 3. In this paper, we construct a complete list of irreducible projective\n(or spin) representations of $G$ and compute their characters (called spin\ncharacters). It is a continuation of our study of spin representations in the\ncases where $M(G)$ contains prime number 2 to the cases where other prime $p$\nappears, firstly $p=3$. We classify irreducible spin representations and\ncalculate spin characters according to their spin types.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"46 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Projective (or spin) representations of finite groups. II\",\"authors\":\"Tatsuya Tsurii, Satoe Yamanaka, Itsumi Mikami, Takeshi Hirai\",\"doi\":\"arxiv-2408.03486\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the previous paper, we proposed a practical method of constructing\\nexplicitly representation groups $R(G)$ for finite groups $G$, and apply it to\\ncertain typical finite groups $G$ with Schur multiplier $M(G)$ containing prime\\nnumber 3. In this paper, we construct a complete list of irreducible projective\\n(or spin) representations of $G$ and compute their characters (called spin\\ncharacters). It is a continuation of our study of spin representations in the\\ncases where $M(G)$ contains prime number 2 to the cases where other prime $p$\\nappears, firstly $p=3$. We classify irreducible spin representations and\\ncalculate spin characters according to their spin types.\",\"PeriodicalId\":501038,\"journal\":{\"name\":\"arXiv - MATH - Representation Theory\",\"volume\":\"46 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-07\",\"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-2408.03486\",\"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 - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03486","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在上一篇论文中,我们提出了一种为有限群 $G$ 明确构造表示群 $R(G)$ 的实用方法,并将其应用于某些典型的有限群 $G$ ,其舒尔乘数 $M(G)$ 包含初数 3。在本文中,我们构建了 $G$ 不可还原的投影(或自旋)表示的完整列表,并计算了它们的字符(称为自旋字符)。这是我们在 $M(G)$ 包含素数 2 的情况下对自旋表示的研究的延续,也是其他素数 $p$ 出现的情况的延续,首先是 $p=3$。我们对不可还原自旋表示进行分类,并根据它们的自旋类型计算自旋字符。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Projective (or spin) representations of finite groups. II
In the previous paper, we proposed a practical method of constructing explicitly representation groups $R(G)$ for finite groups $G$, and apply it to certain typical finite groups $G$ with Schur multiplier $M(G)$ containing prime number 3. In this paper, we construct a complete list of irreducible projective (or spin) representations of $G$ and compute their characters (called spin characters). It is a continuation of our study of spin representations in the cases where $M(G)$ contains prime number 2 to the cases where other prime $p$ appears, firstly $p=3$. We classify irreducible spin representations and calculate spin characters according to their spin types.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Multiprojective Seshadri stratifications for Schubert varieties and standard monomial theory Knot theory and cluster algebra III: Posets Topological K-theory of quasi-BPS categories for Higgs bundles Generalizations of the fractional Fourier transform and their analytic properties Indecomposability and irreducibility of monomial representations for set-theoretical solutions to the Yang-Baxter equation
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1