论文标题
关于伊瓦霍里派代表的区别
On the distinction of Iwahori-spherical representations
论文作者
论文摘要
令$ e/f $为非架构的非围场本地字段和$ \ mathbb h $ a简单连接的半imimple代数组的二次未施加扩展，定义并分配了$ f $。我们在$ \ hh（f）$ - $ \ hh（e）$的iWahori-Spherical表示形式上建立了一般结果（倍增性，测试向量）。对于$ \ hh（e）$的离散系列iWahori-Spherical表示，我们证明了$ \ hh（f）$ - 区别的数值标准。作为一个应用程序，我们将$ \ hh（e）$的$ \ hh（f）$ - 杰出的离散系列表示形式对应于iwahori-hecke代数的学位$ 1 $字符。
Let $E/F$ be a quadratic unramified extension of non-archimedean local fields and $\mathbb H$ a simply connected semisimple algebraic group defined and split over $F$. We establish general results (multiplicities, test vectors) on $\HH (F)$-distinguished Iwahori-spherical representations of $\HH (E)$. For discrete series Iwahori-spherical representations of $\HH (E)$, we prove a numerical criterion of $\HH (F)$-distinction. As an application, we classify the $\HH (F)$-distinguished discrete series representations of $\HH (E)$ corresponding to degree $1$ characters of the Iwahori-Hecke algebra.
