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arXiv · 2303.08267

Koszul duality for Coxeter groups

Simon Riche·Cristian Vay
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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 $(W,S)$ attached to the dual realization.

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Simon Riche, Cristian Vay. 2023-03-14. Koszul duality for Coxeter groups. https://arxiv.org/abs/2303.08267

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