Koszul duality for Coxeter groups
Riche, Simon1; Vay, Cristian2
1 Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
2 Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, CIEM–CONICET, Córdoba, Argentina
Annals of Representation Theory, Volume 1 (2024) no. 3, pp. 335-374.

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 Beĭlinson–Ginzburg–Soergel [8] and Bezrukavnikov–Yun [9] in a geometric context, and of the first author with Achar, Makisumi and Williamson [4]. As an application, we show that the combinatorics of the “tilting perverse sheaves” considered in [6] 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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DOI: 10.5802/art.10
Classification: 18M30, 20C08, 20F55, 16S37
Keywords: Koszul duality, Coxeter group, Elias–Williamson diagrammatic category, Hecke category, Highest weight categories, Perverse sheaves
Riche, Simon 1; Vay, Cristian 2

1 Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
2 Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, CIEM–CONICET, Córdoba, Argentina
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Riche, Simon; Vay, Cristian. Koszul duality for Coxeter groups. Annals of Representation Theory, Volume 1 (2024) no. 3, pp. 335-374. doi : 10.5802/art.10. https://art.centre-mersenne.org/articles/10.5802/art.10/

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