The Glauberman correspondence is a fundamental bijection in the character theory of finite groups. In 1994, Hartley and Turull established a degree-divisibility property for characters related by that correspondence, subject to a congruence condition which should hold for the Green functions of finite groups of Lie type, as defined by Deligne and Lusztig. Here, we present a general argument for completing the proof of that congruence condition. Consequently, the degree-divisibility property holds in complete generality.

中文翻译：

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格林函数和格劳伯曼度可分性

格劳伯曼对应是有限群特征论中的基本双射。1994 年，Hartley 和 Turull 为与该对应关系相关的字符建立了一个度可分性属性，服从于 Deligne 和 Lusztig 定义的 Lie 类型有限群的格林函数应该成立的同余条件。在这里，我们提出了完成该同余条件证明的一般论据。因此，度可分性具有完全的一般性。