数学物理学报(英文版)

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THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

杨乔华; 张钦   

  1. 中国科学院武汉物理与数学所, 武汉 430071
  • 收稿日期:2004-11-15 修回日期:2005-08-29 出版日期:2007-10-20 发布日期:2007-10-20
  • 通讯作者: 杨乔华
  • 基金资助:

    This work was supported by Nalional Science Foundation of China (10571044)

THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

Yang Qiaohua; Zhang Qin   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • Received:2004-11-15 Revised:2005-08-29 Online:2007-10-20 Published:2007-10-20
  • Contact: Yang Qiaohua

摘要:

Let G=SU(2,2), K=S(U(2)×U(2)), and for l∈Z, let {τl}l∈Z be a one-dimensional K-type and let El be the line bundle over G/K associated to τl. It is shown that the τl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.

关键词: Spherical function, central limit theorem, hypergeometric function

Abstract:

Let G=SU(2,2), K=S(U(2)×U(2)), and for l∈Z, let {τl}l∈Z be a one-dimensional K-type and let El be the line bundle over G/K associated to τl. It is shown that the τl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.

Key words: Spherical function, central limit theorem, hypergeometric function

中图分类号: 

  • 22E30