Stable vectors in Moy–Prasad filtrations
Stable vectors in Moy–Prasad filtrations
复制标题
Moy–Prasad 过滤中的稳定载体
DOI：
10.1112/s0010437x16008228
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发表时间：
2015
影响因子：
1.8
通讯作者：
Beth Romano
中科院分区：
文献类型：
--
作者：
Jessica Fintzen;Beth Romano
设$k$是$\mathbb{Q}_{p}$的一个有限扩展，设${\mathcal{G}}$是$k$上的一个绝对简单分裂约化群，设$k$是$k$的一个极大无分支扩展。在Bruhat-Tits构造${\mathcal{G}}_{K}$的每个点上，Moy和Prasad通过有界子群附加了${\mathcal{G}}(K)$的过滤。本文给出了第一Moy-Prasad过滤商的对偶包含约化商作用的稳定向量的充分必要条件。我们的工作扩展了Reeder和Yu的早期结果，他们在$p$足够大的情况下给出了分类。如果有必要，通过传递给$k$的有限无分支扩展，我们得到了${\mathcal{G}}(k)$的新的超尖表示。
Let $k$ be a finite extension of $\mathbb{Q}_{p}$ , let ${\mathcal{G}}$ be an absolutely simple split reductive group over $k$ , and let $K$ be a maximal unramified extension of $k$ . To each point in the Bruhat–Tits building of ${\mathcal{G}}_{K}$ , Moy and Prasad have attached a filtration of ${\mathcal{G}}(K)$ by bounded subgroups. In this paper we give necessary and sufficient conditions for the dual of the first Moy–Prasad filtration quotient to contain stable vectors for the action of the reductive quotient. Our work extends earlier results by Reeder and Yu, who gave a classification in the case when $p$ is sufficiently large. By passing to a finite unramified extension of $k$ if necessary, we obtain new supercuspidal representations of ${\mathcal{G}}(k)$ .