{"title":"poincarcarr对偶和Langlands对偶扩展了仿射Weyl群","authors":"Graham A. Niblo, R. Plymen, N. Wright","doi":"10.2140/AKT.2018.3.491","DOIUrl":null,"url":null,"abstract":"In this paper we construct an equivariant Poincar\\'e duality between dual tori equipped with finite group actions. We use this to demonstrate that Langlands duality induces a rational isomorphism between the group $C^*$-algebras of extended affine Weyl groups at the level of $K$-theory.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2017-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/AKT.2018.3.491","citationCount":"4","resultStr":"{\"title\":\"Poincaré duality and Langlands duality for\\nextended affine Weyl groups\",\"authors\":\"Graham A. Niblo, R. Plymen, N. Wright\",\"doi\":\"10.2140/AKT.2018.3.491\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we construct an equivariant Poincar\\\\'e duality between dual tori equipped with finite group actions. We use this to demonstrate that Langlands duality induces a rational isomorphism between the group $C^*$-algebras of extended affine Weyl groups at the level of $K$-theory.\",\"PeriodicalId\":42182,\"journal\":{\"name\":\"Annals of K-Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2017-11-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.2140/AKT.2018.3.491\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/AKT.2018.3.491\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/AKT.2018.3.491","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Poincaré duality and Langlands duality for
extended affine Weyl groups
In this paper we construct an equivariant Poincar\'e duality between dual tori equipped with finite group actions. We use this to demonstrate that Langlands duality induces a rational isomorphism between the group $C^*$-algebras of extended affine Weyl groups at the level of $K$-theory.
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