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| 摘要: |
| 本文研究了伪黎曼对称空间SL（n+1，R）/S（GL（1，R）×GL（n，R））线丛上的微分方程.利用李代数方法，即Casimir算子得到这个微分算子.这个微分算子是一个超几何方程，这个结论推广了文献[1，3，5]中的微分方程. |
| 关键词: Casimir算子 伪黎曼对称空间 线丛 超几何方程 |
| DOI： |
| 分类号:O152.5 |
| 基金项目:Supported by the Research Foundation of Education Department of Hubei Province (Q20121512). |
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| A HYPERGEOMETRIC EQUATION ON THE LINE BUNDLE OVER SL(n+1,R)/S(GL(1,R)×GL(n,R)) |
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YANG Xiang-hui,HE Min-hua,ZHU Li
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| Abstract: |
| In this paper, we study the difierential equation on the line bundle over the pseudo-Riemannian symmetric space SL(n + 1,R)/S(GL(1,R)×GL(n,R)). We use Lie algebraic method, i.e., Casimir operator to obtain the desired difierential operator. The difierential equation turns out to be a hypergeometric difierential equation, which generalizes the difierential equations in[1, 3, 5]. |
| Key words: Casimir operator pseudo-Riemannian symmetric space line bundle hypergeometric equation |
