论文标题
显式矩阵系数和测试向量的离散串联表示形式
Explicit matrix coefficients and test vectors for discrete series representations
论文作者
论文摘要
对于非Archimedean Local Field $ f $上$ {\ rm gl}（n）$的离散级数表示，我们为未塑造的主系列定义了类似于“区域球形函数”的函数概念。我们证明在$ 0 $ case中存在此类功能。至于未受到的主体系列，它们会产生明确的系数。我们推断出Matringe的离散系列区别标准的本地证明，在$ 0 $情况下，对于Galois对称空间$ {\ rm gl}（n，n，f）/{\ rm gl}（n，f_0）$，对于任何未造成的QUADRATIC EXTRAGINAL EXTRACINE EXTEMENTION。区分这些表示时，我们还会表现出明确的测试向量。
For the discrete series representations of ${\rm GL}(n)$ over a non-archimedean local field $F$, we define a notion of functions similar to "zonal spherical functions" for unramified principal series. We prove the existence of such functions in the level $0$ case. As for unramified principal series, they give rise to explicit coefficients. We deduce a local proof of Matringe's criterion of distinction of discrete series, in the level $0$ case, for the Galois symmetric space ${\rm GL}(n,F)/{\rm GL}(n,F_0 )$, for any unramified quadratic extension $F/F_0$. We also exhibit explicit test vectors when these representations are distinguished.
