Abstract We generalize the Alvis–Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis–Curtis duality of infinite type, which we define in this paper, also interchanges the irreducible representations in the principal representation category.

中文翻译：

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用 Frobenius 映射表示约简群的 Alvis-Curtis 对偶性

摘要 我们将 Alvis-Curtis 对偶性推广到具有 Frobenius 映射的还原群的抽象表示。与有限还原群表示的情况类似，我们证明了我们在本文中定义的无限类型的 Alvis-Curtis 对偶性也可以交换主表示类别中的不可约表示。