Alvis-Curtis duality as an equivalence of derived categories

M Cabanes, JC Rickard

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

Abstract

Let G be the group of rational points of a connected reductive group defined over a finite field of characteristic p, and let O be any commutative ring in which p is invertible. We prove that the duality operation of Alvis, Curtis, Kawanka and Lusztig on the characters of G is induced by a self-equivalence of the derived category of OG-modules, which was conjectured by Broue. We also prove that this equivalence of derived categories is compatible with Harish-Chandra induction and truncation.
Translated title of the contributionAlvis-Curtis duality as an equivalence of derived categories
Original languageEnglish
Title of host publicationModular Representation Theory of Finite Groups
EditorsMichael J Collins, Brian Parshall, Leonard L Scott
Publisherde Gruyter
Pages157 - 174
Number of pages18
ISBN (Print)3110163675
Publication statusPublished - 2001

Bibliographical note

Other identifier: 9783110163674

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    Cabanes, M., & Rickard, JC. (2001). Alvis-Curtis duality as an equivalence of derived categories. In M. J. Collins, B. Parshall, & L. L. Scott (Eds.), Modular Representation Theory of Finite Groups (pp. 157 - 174). de Gruyter.