Koszul duality for Coxeter groups
arXiv:2303.08267
Abstract
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 attached to the dual realization.
v2: We corrected an issue with gradings in Section 5 by introducing properly the karoubian closure of the category FM(h,W) in Section 4.8. This is the final version accepted in Annals of Representation Theory