{"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}
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.