论文标题
$ p $ - 亚种四元基金矩阵的球形功能和局部密度
Spherical functions and local densities on the space of $p$-adic quaternion hermitian matrices
论文作者
论文摘要
我们介绍了$ {\ Mathfrak p} $上的Quaternion Hermitian Shiemian Shiemian尺寸$ n $的空间$ x $，具有奇怪的残留特征，并在$ x $上定义了典型的球形函数$ x（x; s）$，并使用Quaternion Herderian Herdernion Herdernion Herdernion Herdernion Herdernion Herdernion Herdernion Herdernion Herdernion Herdien shize y sige y s $ x $。然后，我们给出有关$ s_n $的球形函数功能方程，并确定$ω（x; s）$的明确公式。另一方面，我们定义了基于$ω（x; s）$的Schwartz Space $ {\ Mathcal s} $ {\ Mathcal s} $的球形变换，并研究$ {\ Mathcal S}的Hecke模块结构（k \ backslash x）$。
We introduce the space $X$ of quaternion hermitian forms of size $n$ on a ${\mathfrak p}$-adic field with odd residual characteristic, and define typical spherical functions $ω(x;s)$ on $X$ and give their induction formula on sizes by using local densities of quaternion hermitian forms. Then we give functional equation of spherical functions with respect to $S_n$, and determine the explicit formulas of $ω(x;s)$. On the other hand, we define the spherical transform on the Schwartz space ${\mathcal S}(K\backslash X)$ based on $ω(x; s)$ and study the Hecke module structure of ${\mathcal S}(K \backslash X)$.
