论文标题
$ \ mathrm {gl} _ {n}（f）$以正交互动区分
Supercuspidal representations of $\mathrm{GL}_{n}(F)$ distinguished by an orthogonal involution
论文作者
论文摘要
令$ f $为残基特征的非一切本紧凑型$ p \ neq2 $，令$ g = \ m atrm {gl} _ {n}（f）$，让$ h $为$ g $的正交子组。对于$π$，$ g $的复杂平滑的超舒张表示形式，我们为杰出的空间$ \ mathrm {hom} _ {h} _ {h}（π，1）$完全表征非零，我们进一步研究了其尺寸为复杂的矢量空间，这将Hakim的类似结果用于Tame SuperCuspidal的Hakim的相似结果。作为推论，作为复杂的矢量空间，$ g $中平滑函数的$π$的嵌入在平滑函数的空间中，是非零的，并且仅当$π$评估$ -1 $ -1 $的核心特征是$ 1 $的，而$π$的中心特征是$ 1 $。
Let $F$ be a non-archimedean locally compact field of residue characteristic $p\neq2$, let $G=\mathrm{GL}_{n}(F)$ and let $H$ be an orthogonal subgroup of $G$. For $π$ a complex smooth supercuspidal representation of $G$, we give a full characterization for the distinguished space $\mathrm{Hom}_{H}(π,1)$ being non-zero and we further study its dimension as a complex vector space, which generalizes a similar result of Hakim for tame supercuspidal representations. As a corollary, the embeddings of $π$ in the space of smooth functions on the set of symmetric matrices in $G$, as a complex vector space, is non-zero and of dimension four, if and only if the central character of $π$ evaluating at $-1$ is $1$.
