In this paper we verify Navarro's refinement of the McKay conjecture for quasi-simple groups of Lie type in their defining characteristic. Navarro's refinement takes into account the action of specific Galois automorphisms on the characters presents in the McKay conjecture [12]. Our proof of this case of the conjecture relies on a character correspondence constructed by Maslowski in [11]. Building on this we verify the inductive condition for Navarro's refinement from [14] for most groups of Lie type in defining characteristic.

中文翻译：

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定义特征的有限Lie型群的McKay猜想的Navarro改进

在本文中，我们验证了Navarro在拟定类型的Lie型准群上对McKay猜想的改进。Navarro的改进考虑了特定的Galois自同构对McKay猜想中出现的字符的作用[12]。我们对此猜想情况的证明依赖于Maslowski在[11]中构造的字符对应关系。在此基础上，我们针对定义特征的大多数Lie类型组从[14]验证了Navarro细化的归纳条件。