We describe the twisted doubling integrals of Cai–Friedberg–Ginzburg–Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so, we define a family of degenerate Whittaker coefficients that are suitable in this setup and study some of their properties. We also prove certain related global and local results that use the same tools.

中文翻译：

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经典群的扭曲加倍积分

我们以概念方式描述了 Cai-Friedberg-Ginzburg-Kaplan 的扭曲加倍积分。这也将构造扩展到四元单一基团。我们在本文中统一进行展开论证。为此，我们定义了一系列适用于此设置的退化 Whittaker 系数，并研究了它们的一些属性。我们还证明了使用相同工具的某些相关的全局和本地结果。