Normality of Some Nilpotent Varieties and Cohomology of Line Bundles on the Cotangent Bundle of the Flag Variety

摘要: Let G be a connected, complex reductive group and B, Borel subgroup. The homogeneous space G/B is called the (full) flag variety of G; for GL n this ordinary flags subspaces in ℂ . properties have many implications study groups their representations. For example, all irreducible finite dimensional G-modules can obtained as global sections line bundles on variety. More generally, any its (G-linearized) has at most one non-vanishing sheaf-cohomology space, having natural structure simple G-module if simply connected. This part content Borel-Weil-Bott theorem seen geometric interpretation E. Cartan’s theory highest weights.