2024/11/04 by Rızacan Çiloğlu, Çiloğlu, Rızacan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2411.02648
openalex publication_date 2024/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a description of Iwahori-Whittaker equivariant perverse sheaves on affine flag varieties associated to tamely ramified reductive groups, in terms of Langlands dual data. This extends the work of Arkhipov-Bezrukavnikov from the case of split reductive groups. To achieve this, we first extend the theory of Wakimoto sheaves to our context and prove convolution exact central objects admit a filtration by such. We then establish the tilting property of the Iwahori-Whittaker averaging of certain central objects arising from the geometric Satake equivalence, which enables us to address the absence of an appropriate analogue of Gaitsgory's central functor for non-split groups.