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数学与物理学

求CP的SU(2)轨道的根分布方法

  • 李小虎 ,
  • 肖良
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  • 中国科学院大学数学科学学院, 北京 100049

收稿日期: 2015-09-28

  修回日期: 2016-01-27

  网络出版日期: 2016-07-15

基金资助

国家自然科学基金(11331002)资助

Study of SU(2)-orbit in CPn based on root distribution

  • LI Xiaohu ,
  • XIAO Liang
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  • School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2015-09-28

  Revised date: 2016-01-27

  Online published: 2016-07-15

摘要

从根分布的角度,对齐性二维球面分类结果给出比Bando和Ohnita(J Math Soc Japan,1987,39:477)更加明显的刻画,求出决定齐性二维球面的SU(2)轨道的李群多项式表示的显式表达式,证明复射影空间中SU(2)轨道的维数取决于一个对应的扩大复平面系数上的一元n次方程的重根和负共轭倒数根对分布,把SU(2)轨道维数归结为黎曼球面上n个点是否重合或成为对径点的问题。也初步研究了SU(2)三维轨道性质与根分布的关系。

本文引用格式

李小虎 , 肖良 . 求CP的SU(2)轨道的根分布方法[J]. 中国科学院大学学报, 2016 , 33(4) : 438 -442 . DOI: 10.7523/j.issn.2095-6134.2016.04.002

Abstract

We obtain a more explicit expression than Bando-Ohnita (J Math Soc Japan, 1987, 39:477) for judging that a SU(2)-orbit is a two-dimension homogeneous sphere, based on the root distribution, and study the SU(2)-orbit problem in CPn by checking whether some n-points are collinear on a Riemann sphere.

参考文献

[1] Bando S,Ohnita Y.Minimal 2-spheres with constant curvature in CPn [J].J Math Soc Japan,1987,39(3):477-487.
[2] Fei J,Jiao X X,Xiao L, et al.On the classification of homogeneous 2-spheres in complex Grassmannians[J].Osaka J Math, 2013,50:135-152.
[3] Li H Z,Wang C P,Wu F E.The classification of homogeneous 2-spheres in CPn [J].Asian Journal of Mathematics,2001,5(1):93-108.
[4] Jiao X X,Peng J G.On minimal two-spheres in G(2; 4)[J].Front Math China, 2010,5(2):297-310.
[5] Fei J,Jiao X X,Xu X W.On conformal minimal 2-spheres in complex Grassmann manifold G(2; n)[J].Proc Indian Acad Sci(Math Sci),2011,121(2):181-199.
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