经典群低复杂度双旗变的Cox环不变量

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2015-01-01 DOI:10.1090/MOSC/244

E. Ponomareva

{"title":"经典群低复杂度双旗变的Cox环不变量","authors":"E. Ponomareva","doi":"10.1090/MOSC/244","DOIUrl":null,"url":null,"abstract":"We find the algebras of unipotent invariants of Cox rings for all double flag varieties of complexity 0 and 1 for the classical groups; namely, we obtain presentations of these algebras. It is well known that such an algebra is simple in the case of complexity 0. We show that, in the case of complexity 1, the algebra in question is either a free algebra or a hypersurface. Knowing the structure of this algebra permits one to effectively decompose tensor products of irreducible representations into direct sums of irreducible representations.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"193 1","pages":"71-133"},"PeriodicalIF":0.0000,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/244","citationCount":"11","resultStr":"{\"title\":\"Invariants of the Cox rings of low-complexity double flag varieties for classical groups\",\"authors\":\"E. Ponomareva\",\"doi\":\"10.1090/MOSC/244\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We find the algebras of unipotent invariants of Cox rings for all double flag varieties of complexity 0 and 1 for the classical groups; namely, we obtain presentations of these algebras. It is well known that such an algebra is simple in the case of complexity 0. We show that, in the case of complexity 1, the algebra in question is either a free algebra or a hypersurface. Knowing the structure of this algebra permits one to effectively decompose tensor products of irreducible representations into direct sums of irreducible representations.\",\"PeriodicalId\":37924,\"journal\":{\"name\":\"Transactions of the Moscow Mathematical Society\",\"volume\":\"193 1\",\"pages\":\"71-133\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/MOSC/244\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Moscow Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/MOSC/244\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/MOSC/244","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 11

摘要

对经典群的复杂度为0和1的所有双标志变异，我们得到了Cox环的单不变量代数;也就是说，我们得到了这些代数的表示。众所周知，这样的代数在复杂度为0的情况下是简单的。我们证明，在复杂度为1的情况下，所讨论的代数要么是自由代数，要么是超曲面。知道这个代数的结构允许人们有效地将不可约表示的张量积分解为不可约表示的直接和。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Invariants of the Cox rings of low-complexity double flag varieties for classical groups

We find the algebras of unipotent invariants of Cox rings for all double flag varieties of complexity 0 and 1 for the classical groups; namely, we obtain presentations of these algebras. It is well known that such an algebra is simple in the case of complexity 0. We show that, in the case of complexity 1, the algebra in question is either a free algebra or a hypersurface. Knowing the structure of this algebra permits one to effectively decompose tensor products of irreducible representations into direct sums of irreducible representations.

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

来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

自引率

0.00%

发文量

期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.