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

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.

9 pages, accepted by Forum Mathematicum