We study representations of the general and the special linear groups over a non-archimedean local field that admit a non-zero invariant linear form with respect to the symplectic group (henceforth distinguished representations). For the class of ladder representations that are distinguished we show that applying the highest derivative operation twice results in a distinguished (ladder) representation. Furthermore, we characterize the unique distinguished component of the associated L-packet of representations of the special linear group in terms of the associated maximal unipotent orbit. We also obtain a sufficient condition for distinction of standard modules.

中文翻译：

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关于辛周期和对 SL(2n) 的限制

我们研究了非阿基米德局部域上的一般和特殊线性群的表示，该域允许相对于辛群的非零不变线性形式（以下称为区分表示）。对于区分的梯形表示类，我们表明两次应用最高导数运算会导致区分（梯形）表示。此外，我们根据相关的最大单能轨道来表征特殊线性群表示的相关 L 数据包的唯一可区分组件。我们也得到了区分标准模块的充分条件。