2-row Springer Fibres and Khovanov Diagram Algebras for Type D
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 cohomolo...
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Veröffentlicht in: | Canadian journal of mathematics 2016-12, Vol.68 (6), p.1285-1333 |
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Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | 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. |
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ISSN: | 0008-414X 1496-4279 |
DOI: | 10.4153/CJM-2015-051-4 |