2-row Springer Fibres and KhovanovDiagram Algebras for Type D

Ehrig, Michael ; Stroppel, Catharina

Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1285-1333

Résumé

We 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 ${{\mathbb{P}}^{1}}$ -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 $\text{D}$ 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 $\text{D}$ setting and should be seen as setting the framework for generalizing well-known connections of these algebras in type $\text{A}$ to other types.

Détail

DOI : 10.4153/CJM-2015-051-4

Mots-clés : 17-11, Springer fibers, Khovanov homology, Weyl group type D

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