Abstract Suppose that F is a non-Archimedean local field of characteristic not 2 and D is a central division algebra over F. Let n be a positive integer. We show a classification modulo essentially square-integrable representations of standard modules of GL n ( D ) which have non-zero linear periods. By this classification, the conjecture of Prasad and Takloo-Bighash is reduced to the case of essentially square-integrable representations.

中文翻译：

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线性周期标准模块的分类

摘要 假设 F 是特征不为 2 的非阿基米德局部域，D 是 F 上的中心除法代数。设 n 为正整数。我们展示了具有非零线性周期的 GL n ( D ) 的标准模的分类模基本上平方可积的表示。通过这种分类，Prasad 和 Takloo-Bighash 的猜想被简化为基本上平方可积表示的情况。