论文标题
$ p $ adic-adic主体系列表示形式中的刚性矢量
Rigid vectors in $p$-adic principal series representations
论文作者
论文摘要
在本文中，我们将Pro-P $ iwahori子组$ i $视为刚性分析组$ \ bbb {i} $，适合足够大$ p $。这是通过将$ i $赋予天然$ p $价值的$ i $来完成的，从而将lazard的结果概括为$ \ text {gl} _n $。我们在某些$ p $ -ADIC字段（简单地连接的派生群体）上与一个通用连接的还原分组合作，并研究$ \ bbb {i} $ - 主要系列表示中的分析向量。我们的主要结果是一个不可约性标准，它在$ \ text {gl} _n $ -case中概括了clozel和ray的结果。
In this paper we view pro-$p$ Iwahori subgroups $I$ as rigid analytic groups $\Bbb{I}$ for large enough $p$. This is done by endowing $I$ with a natural $p$-valuation, and thereby generalizing results of Lazard for $\text{GL}_n$. We work with a general connected reductive split group over some $p$-adic field (with simply connected derived group) and study the $\Bbb{I}$-analytic vectors in principal series representations. Our main result is an irreducibility criterion which generalizes results of Clozel and Ray in the $\text{GL}_n$-case.
