We use the theta lifts between [Formula: see text] and [Formula: see text] to study the distinction problems for the pair [Formula: see text] where [Formula: see text] is a quadratic field extension over a nonarchimedean local field [Formula: see text] of characteristic zero and [Formula: see text] is a quaternion algebra. With a similar strategy, we give a conjectural formula for the multiplicity of distinction problem related to the pair [Formula: see text]

中文翻译：

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Metaplectic case的区分问题

我们使用 [Formula: see text] 和 [Formula: see text] 之间的 theta lifts 来研究对 [Formula: see text] 的区分问题，其中 [Formula: see text] 是非阿基米德局部域上的二次域扩展[公式：见正文]特征零和[公式：见正文]是四元数代数。用类似的策略，我们给出了一个关于对的多重性问题的猜想公式[公式：见正文]