Endoscopy for affine Hecke categories
摘要
We show that the neutral block of the affine monodromic Hecke category for a reductive group is monoidally equivalent to the neutral block of the affine Hecke category for its endoscopic group. The semisimple complexes of both categories can be identified with the generalized Soergel bimodules via the Soergel functor. We extend this identification of semisimple complexes to the neutral blocks of the affine Hecke categories by the technical machinery developed by Bezrukavnikov and Yun.