2023/01/13 by A. N. Ionov, Ionov, Andrei, Zhiwei Yun +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2301.05409
openalex publication_date 2023/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a certain class of real analytic varieties with Lie group actions we develop a theory of (free-monodromic) tilting sheaves, and apply it to flag varieties stratified by real group orbits. For quasi-split real groups, we construct a fully faithful embedding of the category of tilting sheaves to a real analog of the category of Soergel bimodules, establishing real group analogs of Soergel's Structure Theorem and Endomorphism Theorem. We apply these results to give a purely geometric proof of the theorem of Bezrukavnikov and Vilonen which proves Soergel's conjecture for quasi-split groups.