The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain automorphic representations of general linear groups. It is a question of J. Arthur and W. Schmid that asks: How to construct concrete modules for irreducible cuspidal automorphic representations of classical groups in term of their global Arthur parameters? In this paper, we formulate a general construction of concrete modules, using Bessel periods, for cuspidal automorphic representations of classical groups with generic global Arthur parameters. Then we establish the theory for orthogonal and unitary groups, based on certain well-expected conjectures. Among the consequences of the theory in this paper is that the global Gan-Gross-Prasad conjecture for those classical groups is proved in full generality in one direction and with a global assumption in the other direction.

中文翻译：

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经典群的亚瑟参数和尖点自守模

通过稳定迹公式比较的内窥镜分类提供了经典群的不可约尖点自守表示与其全局亚瑟参数之间的某些特征关系，这是一般线性群的某些自守表示。这是 J. Arthur 和 W. Schmid 提出的问题：如何根据全局 Arthur 参数为经典群的不可约尖点自守表示构建具体模块？在本文中，我们使用贝塞尔周期制定了具体模块的一般构造，用于具有通用全局 Arthur 参数的经典群的尖点自守表示。然后我们建立了正交群和酉群的理论，基于某些很好的猜想。