Modules over the small quantum group and semi-infinite flag manifold

2005/05/13 by Sergey Arkhipov, S. Arkhipov, R. Bezrukavnikov +12
Mathematics · #14H60 #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14H60 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0505280

arxiv created 2005/05/13 · openalex publication_date 2005/05/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a theory of perverse sheaves on the semi-infinite flag manifold G((t))/N((t))⋅ T[[t]], and show that the subcategory of Iwahori-monodromy perverse sheaves is equivalent to the regular block of the category of representations of the small quantum group at an even root of unity.

Citations

• Geometric Langlands duality and representations of algebraic groups over commutative rings

Related

• The half-quantum flag variety and representations for small quantum groups
• Another realization of the category of modules over the small quantum group
• An introduction to perverse sheaves
• Quantum Groups, the loop Grassmannian, and the Springer resolution
• The small quantum group and the Springer resolution