单李群幂零轨道的逼近

IF 0.5 4区 数学 Q3 MATHEMATICS Glasnik Matematicki Pub Date : 2021-01-21 DOI:10.3336/gm.56.2.06
Lucas Fresse, S. Mehdi
{"title":"单李群幂零轨道的逼近","authors":"Lucas Fresse, S. Mehdi","doi":"10.3336/gm.56.2.06","DOIUrl":null,"url":null,"abstract":"We propose a systematic and topological study of limits \\(\\lim_{\\nu\\to 0^+}G_\\mathbb{R}\\cdot(\\nu x)\\) of continuous families of adjoint orbits for a non-compact simple real Lie group \\(G_\\mathbb{R}\\). This limit is always a finite union of nilpotent orbits. We describe explicitly these nilpotent orbits in terms of Richardson orbits in the case of hyperbolic semisimple elements. We also show that one can approximate minimal nilpotent orbits or even nilpotent orbits by elliptic semisimple orbits. The special cases of \\(\\mathrm{SL}_n(\\mathbb{R})\\) and \\(\\mathrm{SU}(p,q)\\) are computed in detail.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Approximation of nilpotent orbits for simple Lie groups\",\"authors\":\"Lucas Fresse, S. Mehdi\",\"doi\":\"10.3336/gm.56.2.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a systematic and topological study of limits \\\\(\\\\lim_{\\\\nu\\\\to 0^+}G_\\\\mathbb{R}\\\\cdot(\\\\nu x)\\\\) of continuous families of adjoint orbits for a non-compact simple real Lie group \\\\(G_\\\\mathbb{R}\\\\). This limit is always a finite union of nilpotent orbits. We describe explicitly these nilpotent orbits in terms of Richardson orbits in the case of hyperbolic semisimple elements. We also show that one can approximate minimal nilpotent orbits or even nilpotent orbits by elliptic semisimple orbits. The special cases of \\\\(\\\\mathrm{SL}_n(\\\\mathbb{R})\\\\) and \\\\(\\\\mathrm{SU}(p,q)\\\\) are computed in detail.\",\"PeriodicalId\":55601,\"journal\":{\"name\":\"Glasnik Matematicki\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-01-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Glasnik Matematicki\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3336/gm.56.2.06\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasnik Matematicki","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.56.2.06","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2

摘要

对非紧单实李群\(G_\mathbb{R}\)的伴随轨道连续族极限\(\lim_{\nu\to 0^+}G_\mathbb{R}\cdot(\nu x)\)进行了系统的拓扑研究。这个极限总是幂零轨道的有限并。在双曲半单元的情况下,我们用理查德森轨道明确地描述了这些幂零轨道。我们还证明了可以用椭圆半单轨道近似最小幂零轨道或甚至幂零轨道。对\(\mathrm{SL}_n(\mathbb{R})\)和\(\mathrm{SU}(p,q)\)的特殊情况进行了详细的计算。
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Approximation of nilpotent orbits for simple Lie groups
We propose a systematic and topological study of limits \(\lim_{\nu\to 0^+}G_\mathbb{R}\cdot(\nu x)\) of continuous families of adjoint orbits for a non-compact simple real Lie group \(G_\mathbb{R}\). This limit is always a finite union of nilpotent orbits. We describe explicitly these nilpotent orbits in terms of Richardson orbits in the case of hyperbolic semisimple elements. We also show that one can approximate minimal nilpotent orbits or even nilpotent orbits by elliptic semisimple orbits. The special cases of \(\mathrm{SL}_n(\mathbb{R})\) and \(\mathrm{SU}(p,q)\) are computed in detail.
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
Glasnik Matematicki
Glasnik Matematicki MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
0.80
自引率
0.00%
发文量
11
审稿时长
>12 weeks
期刊介绍: Glasnik Matematicki publishes original research papers from all fields of pure and applied mathematics. The journal is published semiannually, in June and in December.
期刊最新文献
On homotopy nilpotency Approximation of nilpotent orbits for simple Lie groups A complete system of the shapes of triangles On the existence of a solution of a class of non-stationary free boundary problems Global integrability for solutions to boundary value problems of anisotropic functionals
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1