{"title":"邻接轨道的合理性","authors":"Vladimir L. Popov","doi":"10.4310/pamq.2024.v20.n1.a11","DOIUrl":null,"url":null,"abstract":"We prove that every orbit of the adjoint representation of any connected reductive algebraic group $G$ is a rational algebraic variety. For complex simply connected semisimple $G$, this implies rationality of homogeneous affine Hamiltonian $G$-varieties (which we classify).","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rationality of adjoint orbits\",\"authors\":\"Vladimir L. Popov\",\"doi\":\"10.4310/pamq.2024.v20.n1.a11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that every orbit of the adjoint representation of any connected reductive algebraic group $G$ is a rational algebraic variety. For complex simply connected semisimple $G$, this implies rationality of homogeneous affine Hamiltonian $G$-varieties (which we classify).\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2024.v20.n1.a11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2024.v20.n1.a11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that every orbit of the adjoint representation of any connected reductive algebraic group $G$ is a rational algebraic variety. For complex simply connected semisimple $G$, this implies rationality of homogeneous affine Hamiltonian $G$-varieties (which we classify).
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