线性周期标准模的分类
Classification of standard modules with linear periods
摘要：
设$F$是非阿基米德局部域，$D$是$F$上的中心除代数.令$n$为正整数。我们展示了一个分类模基本上平方可积表示的标准模块的$\mathrm{GL}_n(D)$具有非零线性周期。通过这种分类，Prasad和Takloo-Bighash的猜想被简化为本质上平方可积〔的〕表示的情形。
英文摘要：
Suppose that $F$ is a non-Archimedean local field 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 $\mathrm{GL}_n(D)$ 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.
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