Alvis-Curtis Duality for Representations of Reductive Groups with Frobenius Maps

2019/07/10 by Junbin Dong, Dong, Junbin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1907.04515

openalex publication_date 2019/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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