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.
Acknowledgements
The author is grateful to Prof. Nanhua Xi for his constant encouragement and guidance. The author thanks Prof. Ming Fang and Dr. Xiaoyu Chen for their useful discussions. The author would also like to thank the referees for careful reading and helpful comments.
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