{"title":"在朗兰双旗变种上的椭圆形类","authors":"Richárd Rimányi, Andrzej Weber","doi":"10.1142/S0219199721500140","DOIUrl":null,"url":null,"abstract":"Characteristic classes of Schubert varieties can be used to study the geometry and the combinatorics of homogeneous spaces. We prove a relation between elliptic classes of Schubert varieties on a generalized full flag variety and those on its Langlands dual. This new symmetry is only revealed if Schubert calculus is elevated from cohomology or K theory to the elliptic level.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Elliptic classes on Langlands dual flag varieties\",\"authors\":\"Richárd Rimányi, Andrzej Weber\",\"doi\":\"10.1142/S0219199721500140\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Characteristic classes of Schubert varieties can be used to study the geometry and the combinatorics of homogeneous spaces. We prove a relation between elliptic classes of Schubert varieties on a generalized full flag variety and those on its Langlands dual. This new symmetry is only revealed if Schubert calculus is elevated from cohomology or K theory to the elliptic level.\",\"PeriodicalId\":278201,\"journal\":{\"name\":\"arXiv: Algebraic Geometry\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Algebraic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/S0219199721500140\",\"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: Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S0219199721500140","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Characteristic classes of Schubert varieties can be used to study the geometry and the combinatorics of homogeneous spaces. We prove a relation between elliptic classes of Schubert varieties on a generalized full flag variety and those on its Langlands dual. This new symmetry is only revealed if Schubert calculus is elevated from cohomology or K theory to the elliptic level.
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