Koszul duality for Coxeter groups - Archive ouverte HAL
Article Dans Une Revue Annals of Representation Theory Année : 2023

Koszul duality for Coxeter groups

Résumé

We construct a "Koszul duality" equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a construction of Beilinson-Ginzburg-Soergel and Bezrukavnikov-Yun in a geometric context, and of the first author with Achar, Makisumi and Williamson. As an application, we show that the combinatorics of the "tilting perverse sheaves" considered in arXiv:1802.07651 is encoded in the combinatorics of the canonical basis of the Hecke algebra of (W,S) attached to the dual realization.
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hal-04056856 , version 1 (03-04-2023)

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Simon Riche, Cristian Vay. Koszul duality for Coxeter groups. Annals of Representation Theory, 2023, 1 (3), pp.335-374. ⟨10.5802/art.10⟩. ⟨hal-04056856⟩
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