| THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU（2,2）/S（U（2） × U（2）） |
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| 引用本文： | 杨乔华 张钦. THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU（2,2）/S（U（2） × U（2））[J]. 数学物理学报(B辑英文版), 2007, 27(4): 867-874. DOI: 10.1016/S0252-9602(07)60084-8 |
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| 作者姓名： | 杨乔华 张钦 |
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| 作者单位： | [1]Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China [2]School of Mathematics and Statistics, Wuhan University, Wuhan 4300＂72, China |
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| 基金项目： | This work was supported by Nalional Science Foundation of China （10571044） |
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| 摘 要： | Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-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.
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| 关 键 词： | 球形函数 中心限制定理 超几何函数 G/K空间 |
| 收稿时间： | 2004-11-15 |
| 修稿时间： | 2004-11-15 |
The spherical functions and the Central limit theorem on SU(2,2)/S(U(2)× U(2)) |
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| Yang Qiaohua,Zhang Qin. The spherical functions and the Central limit theorem on SU(2,2)/S(U(2)× U(2))[J]. Acta Mathematica Scientia, 2007, 27(4): 867-874. DOI: 10.1016/S0252-9602(07)60084-8 |
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| Authors: | Yang Qiaohua Zhang Qin |
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| Affiliation: | Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China ; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| 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 τ1. 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. |
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| Keywords: | Spherical function central limit theorem hypergeometric function |
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