颤振子表示的角条件和矩映射

Pub Date : 2023-11-20 DOI:10.4310/pamq.2023.v19.n4.a1

Velleda Baldoni, Michèle Vergne, Michael Walter

{"title":"颤振子表示的角条件和矩映射","authors":"Velleda Baldoni, Michèle Vergne, Michael Walter","doi":"10.4310/pamq.2023.v19.n4.a1","DOIUrl":null,"url":null,"abstract":"We give inductive conditions that characterize the Schubert positions of subrepresentations of a general quiver representation. Our results generalize Belkale’s criterion for the intersection of Schubert varieties in Grassmannians and refine Schofield’s characterization of the dimension vectors of general subrepresentations. This implies Horn type inequalities for the moment cone associated to the linear representation of the group $G = \\prod_x \\mathrm{GL}(n_x)$ associated to a quiver and a dimension vector $n = (n_x)$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Horn conditions for quiver subrepresentations and the moment map\",\"authors\":\"Velleda Baldoni, Michèle Vergne, Michael Walter\",\"doi\":\"10.4310/pamq.2023.v19.n4.a1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give inductive conditions that characterize the Schubert positions of subrepresentations of a general quiver representation. Our results generalize Belkale’s criterion for the intersection of Schubert varieties in Grassmannians and refine Schofield’s characterization of the dimension vectors of general subrepresentations. This implies Horn type inequalities for the moment cone associated to the linear representation of the group $G = \\\\prod_x \\\\mathrm{GL}(n_x)$ associated to a quiver and a dimension vector $n = (n_x)$.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2023.v19.n4.a1\",\"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.2023.v19.n4.a1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 4

摘要

我们给出了表征一般颤振表示的子表示的舒伯特位置的归纳条件。我们的结果推广了Belkale关于Grassmannians中Schubert变体的交点准则，并改进了Schofield关于一般子表示的维向量的表征。这意味着与群$G = \prod_x \mathrm{GL}(n_x)$的线性表示相关联的力矩锥的Horn型不等式与一个颤振和一个维向量$n = (n_x)$相关联。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Horn conditions for quiver subrepresentations and the moment map

We give inductive conditions that characterize the Schubert positions of subrepresentations of a general quiver representation. Our results generalize Belkale’s criterion for the intersection of Schubert varieties in Grassmannians and refine Schofield’s characterization of the dimension vectors of general subrepresentations. This implies Horn type inequalities for the moment cone associated to the linear representation of the group $G = \prod_x \mathrm{GL}(n_x)$ associated to a quiver and a dimension vector $n = (n_x)$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助