Endoscopy for affine Hecke categories
Yau Wing Li
TL;DR
This paper establishes a monoidal equivalence between the neutral blocks of affine monodromic and affine Hecke categories for reductive groups, linking their semisimple complexes to generalized Soergel bimodules.
Contribution
It extends the identification of semisimple complexes to the neutral blocks of affine Hecke categories using advanced machinery, revealing deep structural connections.
Findings
Neutral blocks are monoidally equivalent
Semisimple complexes correspond to generalized Soergel bimodules
Extension of identification via Bezrukavnikov and Yun's machinery
Abstract
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 the 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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Carbohydrate Chemistry and Synthesis · Molecular spectroscopy and chirality