论文标题
多重性一个定理超过积极特征
Multiplicity one theorems over positive characteristic
论文作者
论文摘要
在[AGR]中，在$ p $ ad的本地田地上，一般线性组，正交组和单一组（$ gl，o，$，$ $）的多个定理被证明是一个定理。也就是说，当我们有一对这样的组时，$ g_n \ subseteq g_ {n+1} $，对$ g_ {n+1} $的不可限制的平滑表示限制到$ g_n $是免费的。该属性已经以$ gl $而闻名，而本地具有积极特征的本地领域，在本文中，我们还提供了$ o，u $和$ $ $ $ $ $ $ $的证明。这些定理在[GGP]中显示，以暗示Bessel模型的独特性，以及在[CS]中暗示Rankin-Selberg模型的独特性。我们还同时在[太阳]中的证明概述之后同时证明了傅里叶雅各比模型的Uniqeuness。根据Gelfand-kazhdan标准，一对$ h \ leq g $的多重属性从$ g $不变的$ h $不变性的任何分布也不变，这也是$ g $保留$ h $ h $的任何不变的。
In [AGRS] a multiplicity one theorem is proven for general linear groups, orthogonal groups and unitary groups ($GL, O,$ and $U$) over $p$-adic local fields. That is to say that when we have a pair of such groups $G_n\subseteq G_{n+1}$, any restriction of an irreducible smooth representation of $G_{n+1}$ to $G_n$ is multiplicity free. This property is already known for $GL$ over a local field of positive characteristic, and in this paper we also give a proof for $O,U$, and $SO$ over local fields of positive odd characteristic. These theorems are shown in [GGP] to imply the uniqueness of Bessel models, and in [CS] to imply the uniqueness of Rankin-Selberg models. We also prove simultaniously the uniqeuness of Fourier-Jacobi models, following the outlines of the proof in [Sun]. By the Gelfand-Kazhdan criterion, the multiplicity one property for a pair $H\leq G$ follows from the statement that any distribution on $G$ invariant to conjugations by $H$ is also invariant to some anti-involution of $G$ preserving $H$.
