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 contribution | Alvis-Curtis duality as an equivalence of derived categories |
|---|---|
| Original language | English |
| Title of host publication | Modular Representation Theory of Finite Groups |
| Editors | Michael J Collins, Brian Parshall, Leonard L Scott |
| Publisher | de Gruyter |
| Pages | 157 - 174 |
| Number of pages | 18 |
| ISBN (Print) | 3110163675 |
| Publication status | Published - 2001 |
Bibliographical note
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Cite this
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.