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arXiv · 2006.15835

Classification of standard modules with linear periods

Miyu Suzuki
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Abstract

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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Miyu Suzuki. 2020-08-17. Classification of standard modules with linear periods. https://doi.org/10.1016/j.jnt.2020.07.005

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