{"title":"正电子变异体与簇代数","authors":"Pavel Galashin, Thomas Lam","doi":"10.24033/asens.2545","DOIUrl":null,"url":null,"abstract":"We show that the coordinate ring of an open positroid variety coincides with the cluster algebra associated to a Postnikov diagram. This confirms conjectures of Postnikov, Muller--Speyer, and Leclerc, and generalizes results of Scott and Serhiyenko--Sherman-Bennett--Williams.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"48 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":"{\"title\":\"Positroid varieties and cluster algebras\",\"authors\":\"Pavel Galashin, Thomas Lam\",\"doi\":\"10.24033/asens.2545\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the coordinate ring of an open positroid variety coincides with the cluster algebra associated to a Postnikov diagram. This confirms conjectures of Postnikov, Muller--Speyer, and Leclerc, and generalizes results of Scott and Serhiyenko--Sherman-Bennett--Williams.\",\"PeriodicalId\":50971,\"journal\":{\"name\":\"Annales Scientifiques De L Ecole Normale Superieure\",\"volume\":\"48 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-10-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"29\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Scientifiques De L Ecole Normale Superieure\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24033/asens.2545\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Scientifiques De L Ecole Normale Superieure","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24033/asens.2545","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We show that the coordinate ring of an open positroid variety coincides with the cluster algebra associated to a Postnikov diagram. This confirms conjectures of Postnikov, Muller--Speyer, and Leclerc, and generalizes results of Scott and Serhiyenko--Sherman-Bennett--Williams.
期刊介绍：
The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics.
Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition.
The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.
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