Spherical characters on P-Adic symmetric spaces
Spherical characters on P-Adic symmetric spaces
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DOI：
10.1353/ajm.1996.0003
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发表时间：
1996-02
影响因子：
1.7
通讯作者：
C. Rader;S. Rallis
中科院分区：
文献类型：
--
作者：
C. Rader;S. Rallis
局部域上的对称空间，以及它们的第一类表示的调和分析，作为雅凯相对迹公式理论的局部计算而出现。在真实的地方有大量的文献，但很少有一般性的结果为p-adic域是已知的。这里的目的是尽可能地将Queens的结果和Howe的前提结果推广到对称空间，并为那些不能推广的东西提供反例。我们得到了Weyl积分公式，θ-正则集上球面特征标的局部不变性，θ-群的Howe猜想，原点球面特征标的芽展开，以及紧p-adic群的Howe Kirillov理论的球面版本.我们发现正则轨道积分的密度性质失效。哈基姆的论文（在埃尔韦雅凯的指导下撰写）中提出了一些基本观点。
Symmetric spaces over local fields, and the harmonic analysis of their class one representations, arise as the local calculation of Jacquet's theory of the relative trace formula. There is an extensive literature at the real place, but few general results for p-adic fields are known. The objective here is to carry over to symmetric spaces as much as possible of Queens and the prerequisite results of Howe, and to provide counterexamples for those things which do not generalize. We derive the Weyl integration formula, local constancy of the spherical character on the θ-regular set, Howe's conjecture for θ-groups, the germ expansion for spherical characters at the origin, and a spherical version of Howe's Kirillov theory for compact p-adic groups. We find that the density property of regular orbital integrals fails. Some of the basic ideas are nascent in Hakim's thesis (written under Herve Jacquet).