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 contribution||Alvis-Curtis duality as an equivalence of derived categories|
|Title of host publication||Modular Representation Theory of Finite Groups|
|Editors||Michael J Collins, Brian Parshall, Leonard L Scott|
|Pages||157 - 174|
|Number of pages||18|
|Publication status||Published - 2001|
Bibliographical noteOther identifier: 9783110163674
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.