{"title":"半单李代数的表示","authors":"Abhinav Shrestha","doi":"10.1090/gsm/193/08","DOIUrl":null,"url":null,"abstract":"This paper studies the representations of semisimple Lie algebras, with care given to the case of sln(C). We develop and utilize various tools, including the adjoint representation, the Killing form, root space decomposition, and the Weyl group to classify the irreducible representations of semisimple Lie algebras.","PeriodicalId":167221,"journal":{"name":"A Tour of Representation Theory","volume":"5 2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Representations of semisimple Lie\\n algebras\",\"authors\":\"Abhinav Shrestha\",\"doi\":\"10.1090/gsm/193/08\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies the representations of semisimple Lie algebras, with care given to the case of sln(C). We develop and utilize various tools, including the adjoint representation, the Killing form, root space decomposition, and the Weyl group to classify the irreducible representations of semisimple Lie algebras.\",\"PeriodicalId\":167221,\"journal\":{\"name\":\"A Tour of Representation Theory\",\"volume\":\"5 2\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"A Tour of Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/gsm/193/08\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"A Tour of Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/gsm/193/08","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper studies the representations of semisimple Lie algebras, with care given to the case of sln(C). We develop and utilize various tools, including the adjoint representation, the Killing form, root space decomposition, and the Weyl group to classify the irreducible representations of semisimple Lie algebras.
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