2025/08/13 by Sandvik, Colton
#14F08 #14F43 #20C08 #20G20 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2508.10214
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.