2015/09/17 by Claude Eicher, Eicher, Claude
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.1509.05299
amsart, 21 pages
arxiv created 2015/09/17 · openalex publication_date 2015/09/17 · arxiv updated 2015/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct twisted D-modules on the projective line ℙ1 that are equivariant for the action of the diagonal torus subgroup of SL2. In the most interesting case these arise as extensions from local systems on ℂ×. We discuss their subquotient structure. Their sheaf cohomology groups are weight modules for the Lie algebra \mathfraksl2. We also discuss their subquotient structure and in case these modules are not the familiar highest or lowest weight modules, we give an explicit presentation for them. Our computations illustrate some basic D-module concepts and the Beilinson-Bernstein equivalence. They are the first step in a program that aims to describe categories of modules over semisimple and affine Kac-Moody Lie algebras that are next to highest (or lowest) weight via D-modules on the flag variety.