Two 2-categories categorify the monodromic Hecke algebra and are proven equivalent, extending Soergel and diagrammatic calculi with links to parity sheaves and endoscopic unipotent categories.
Abe, A bimodule description of the Hecke category, Compos
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Proves the Gorsky-Hogancamp-Mellit-Nakagane conjecture on relative Serre duality for Soergel bimodules of finite Coxeter groups in full generality.
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Soergel calculus for monodromic Hecke categories
Two 2-categories categorify the monodromic Hecke algebra and are proven equivalent, extending Soergel and diagrammatic calculi with links to parity sheaves and endoscopic unipotent categories.
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Relative Serre duality for Coxeter groups
Proves the Gorsky-Hogancamp-Mellit-Nakagane conjecture on relative Serre duality for Soergel bimodules of finite Coxeter groups in full generality.