2-row Springer Fibres and Khovanov Diagram Algebras for Type D

Abstract

AbstractWe study in detail two row Springer fibres of even orthogonal type from an algebraic as well as a topological point of view. We show that the irreducible components and their pairwise intersections are iterated ℙ1-bundles. Using results of Kumar and Procesi we compute the cohomology ring with its action of the Weyl group. The main tool is a type D diagram calculus labelling the irreducible components in a convenient way that relates to a diagrammatical algebra describing the category of perverse sheaves on isotropic Grassmannians based on work of Braden. The diagram calculus generalizes Khovanov's arc algebra to the type D setting and should be seen as setting the framework for generalizing well-known connections of these algebras in type A to other types.