球形亚群的卫星

IF 1.7 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2016-10-24 DOI:10.14231/ag-2020-004

V. Batyrev, Anne Moreau

{"title":"球形亚群的卫星","authors":"V. Batyrev, Anne Moreau","doi":"10.14231/ag-2020-004","DOIUrl":null,"url":null,"abstract":"Let $G$ be a complex connected reductive algebraic group. Given a spherical subgroup $H \\subset G$ and a subset $I$ of the set of spherical roots of $G/H$, we define, up to conjugation, a spherical subgroup $H_I \\subset G$ of the same dimension of $H$, called a satellite. We investigate various interpretations of the satellites. We also show a close relation between the Poincare polynomials of the two spherical homogeneous spaces $G/H$ and $G/H_I$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2016-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Satellites of spherical subgroups\",\"authors\":\"V. Batyrev, Anne Moreau\",\"doi\":\"10.14231/ag-2020-004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $G$ be a complex connected reductive algebraic group. Given a spherical subgroup $H \\\\subset G$ and a subset $I$ of the set of spherical roots of $G/H$, we define, up to conjugation, a spherical subgroup $H_I \\\\subset G$ of the same dimension of $H$, called a satellite. We investigate various interpretations of the satellites. We also show a close relation between the Poincare polynomials of the two spherical homogeneous spaces $G/H$ and $G/H_I$.\",\"PeriodicalId\":48564,\"journal\":{\"name\":\"Algebraic Geometry\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2016-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.14231/ag-2020-004\",\"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":"Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.14231/ag-2020-004","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

设$G$是一个复连通约化代数群。给定$G/H$的球根集合的一个球子群$H \子集G$和一个子集$I$，我们定义一个与$H$具有相同维数的球子群$H_I \子集G$，直到共轭为止，称为卫星。我们研究了对卫星的各种解释。我们还证明了两个球面齐次空间$G/H$和$G/H_I$的庞加莱多项式之间的密切关系。

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

Satellites of spherical subgroups

Let $G$ be a complex connected reductive algebraic group. Given a spherical subgroup $H \subset G$ and a subset $I$ of the set of spherical roots of $G/H$, we define, up to conjugation, a spherical subgroup $H_I \subset G$ of the same dimension of $H$, called a satellite. We investigate various interpretations of the satellites. We also show a close relation between the Poincare polynomials of the two spherical homogeneous spaces $G/H$ and $G/H_I$.

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

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.