标题： 四元数辛模型对于离散系列表示 显示英文标题

标题： Quaternionic symplectic model for discrete series representations

摘要： 设$D$为非阿基米德局部域$F$上的四元数除法代数，其特征为零且剩余特征为奇数。我们证明，$\mathrm{GL}_n(D)$的不可约离散系列表示仅当它是超 cuspidal 时才是$\mathrm{Sp}_n(D)$-区分的。这里，$\mathrm{Sp}_n(D)$是四元数辛群。结合 Sécherre 和 Stevens 对$\mathrm{Sp}_n(D)$-区分的超 cuspidal 表示的最新研究，这完成了如 Dipendra Prasad 所预测的$\mathrm{Sp}_n(D)$-区分的离散系列表示的分类。 显示英文摘要

摘要： Let $D$ be the quatenion division algebra over a non-Archimedean local field $F$ of characteristic zero and odd residual characterisitc. We show that an irreducible discrete series representation of $\mathrm{GL}_n(D)$ is $\mathrm{Sp}_n(D)$-distinguished only if it is supercuspidal. Here, $\mathrm{Sp}_n(D)$ is the quaternionic symplectic group. Combined with the recent study on $\mathrm{Sp}_n(D)$-distinguished supercuspidal representations by S\'echerre and Stevens, this completes the classification of $\mathrm{Sp}_n(D)$-distinguished discrete series representations, as predicted by Dipendra Prasad.