论文标题
连接到单位子组的球形特征的强密度
Strong density of spherical characters attached to unipotent subgroups
论文作者
论文摘要
我们证明了还原性P-ADIC组$ g $的相对表示理论的以下结果： 让$ u $成为$ g $的最小抛物线子组的一能激进，让$ψ$成为$ u $的任意平滑特征。令$ s \ subset Irr（g）$是Zariski致密的$ G $不可约代表的集合。然后，在$ s $上附加到表示上的$π$的bessel发行$b_π$的跨度在空间$ \ mathcal s^*（g）^{u \ times u，ψ\ times u，ψ\ timesψ} $的所有$（u \ \ \ timesψ} $（U \ times u \ times u \ times u \ times u \ times u，ψ\ timesψ\ times 我们基于以下结果的证明： 1。平滑表示的类别$ \ mathcal m（g）$是Cohen-Macaulay。 2。模块$ ind_u^g（ψ）$是一个投影模块。
We prove the following result in relative representation theory of a reductive p-adic group $G$: Let $U$ be the unipotent radical of a minimal parabolic subgroup of $G$, and let $ψ$ be an arbitrary smooth character of $U$. Let $S \subset Irr(G)$ be a Zariski dense collection of irreducible representations of $G$. Then the span of the Bessel distributions $B_π$ attached to representations $π$ from $S$ is dense in the space $\mathcal S^*(G)^{U\times U,ψ\times ψ}$ of all $(U\times U,ψ\times ψ)$-equivariant distributions on $G.$ We base our proof on the following results: 1. The category of smooth representations $\mathcal M(G)$ is Cohen-Macaulay. 2. The module $ind_U^G(ψ)$ is a projective module.
