1999/06/11 by Sergey Arkhipov, Arkhipov, Sergey
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/9906071
20 pages, AMSLaTeX
arxiv created 1999/06/11 · openalex publication_date 1999/06/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we construct some quantum analogues of the global Cousin complex for the flag variety in positive characteristic. Just like in the positive characteristic case, we obtain some remarkable resolutions of the contragradient modules over the small quantum group. We use these resolutions to calculate semiinfinite cohomology of the small quantum group with coefficients in contragradient Weyl modules. It turns out that the described graded space of semiinfinite cohomology is naturally isomorphic to the space of distributions on the cotangent bundle of the flag variety with support in the union of conormal bundles to the Schubert cells with coefficients in the pull-back of a line bundle on the flag variety.