辛群SP（4，R）上的Plancherel定理
Plancherel Theorem on the Symplectic Group SP(4,R)
摘要：
设H是15维连通半单李群，其Iwasawa分解为H.设G是H与四维实向量群的半直积的群。本文的目的是定义傅里叶变换，以得到H上的Plancherel定理，并以此类推G。由于它的10维辛群是H的一个子群，因此容易得到关于它的辛群的Plancherel定理以及关于它的非齐次群的Plancherel定理.为此，我们得到了关于它的幂零辛群的一些有趣的结果
英文摘要：
Let H be the 15- dimensional connected semisimple Lie group with its Iwasawa decomposition of H. Let G be the group of the semi direct product of H and the four dimensional real vector group . The goal of this paper is to define the Fourier transform in order to obtain the Plancherel theorem on H and so on G. Since its symplectic group of dimension 10 is a subgroup of H, then it will be easy to get the Plancherel theorem on the symplectic group and so on its inhomogeneous group. To this end, we obtain some interesting results on its nilpotent symplectic group
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