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.
Endoscopy for Modular Hecke Categories
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abstract
Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this formalism to construct a modular incarnation of Lusztig and Yun's monodromic Hecke category. We then give two applications: (1) a modular categorification of the monodromic Hecke algebra, and (2) a monoidal equivalence between the monodromic Hecke category of parity sheaves and the ordinary Hecke category of parity sheaves on the endoscopic group.
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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.