Components of the Springer fiber and domino tableaux

Pietraho, Thomas

doi:10.1016/s0021-8693(03)00434-4

Cited by 7 publications

(7 citation statements)

References 7 publications

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“…Remark 5.17. Another bijection between signed domino tableaux of a fixed shape and certain standard domino tableaux using cycle moves was established already in [Pie04]. This bijection differs slightly from ours, since we never apply a cycle move to open clusters, thus the shape stays unchanged; we fix instead the parity of the total number of minus signs.…”

Section: Domino Tableaux and Combinatorial Bijectionsmentioning

confidence: 79%

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

Ehrig¹,

Stroppel²

2016

Can. j. math.

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Abstract. We study in detail two row Springer bres of even orthogonal type from an algebraic as well as topological point of view. We show that the irreducible components and their pairwise intersections are iterated P -bundles. Using results of Kumar and Procesi we compute the cohomology ring with its action of the Weyl group.e main tool is a type D diagram calculus labelling the irreducible components in a convenient way which relates to a diagrammatical algebra describing the category of perverse sheaves on isotropic Grassmannians based on work of Braden. e 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.

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Section: Domino Tableaux and Combinatorial Bijectionsmentioning

confidence: 79%

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

Ehrig¹,

Stroppel²

2016

Can. j. math.

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“…We label the new domino by comparing Jordan types of x (i) and x (i+1) with i. More details can be found in [Spa82], [vL89] or [Pie04].…”

Section: Irreducible Components and Combinatoricsmentioning

confidence: 99%

“…In Section 2 we recall basic definitions and facts about the (algebraic) Springer fibers of type C and D and review some known results concerning the combinatorics of the irreducible components. In particular, we review the parameterization of the irreducible components of the Springer fiber in terms of signed domino tableaux as introduced by van Leeuwen in his thesis [vL89] based on earlier work by Spaltenstein [Spa82] (see also [Pie04]).…”

Section: Introductionmentioning

confidence: 99%

Topology of two-row Springer fibers for the even orthogonal and symplectic group

Wilbert

2017

Trans. Amer. Math. Soc.

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We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms a conjecture by Ehrig and Stroppel concerning the topology of the equal-row Springer fiber for the even orthogonal group. Moreover, we show that every two-row Springer fiber for the symplectic group is homeomorphic (even isomorphic as an algebraic variety) to a connected component of a certain two-row Springer fiber for the even orthogonal group.

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“…The irreducible components of Springer fibres in types

B

C

and

D

were first described by Spaltenstein in [, Section II.6], but the combinatorics is quite subtle and involves signed domino tableaux (see also Section 3 of van Leeuwen's thesis for an exposition, and also the simplified version given by Pietraho in ). In , Steinberg constructs a geometric Robinson–Schensted correspondence by looking at the irreducible components of the Steinberg variety in two different ways.…”

Section: Introductionmentioning

confidence: 99%

Irreducible components of exotic Springer fibres

Nandakumar

Rosso

Saunders

2018

J. London Math. Soc.

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Kato introduced the exotic nilpotent cone to be a substitute for the ordinary nilpotent cone of type C with cleaner properties. Here we describe the irreducible components of exotic Springer fibres (the fibres of the resolution of the exotic nilpotent cone), and prove that they are naturally in bijection with standard bitableaux. As a result, we deduce the existence of an exotic Robinson-Schensted bijection, which is a variant of the type C Robinson-Schensted bijection between pairs of same-shape standard bitableaux and elements of the Weyl group; this bijection is described explicitly in the sequel to this paper. Note that this is in contrast with ordinary type C Springer fibres, where the parametrisation of irreducible components, and the resulting geometric Robinson-Schensted bijection, are more complicated. As an application, we explicitly describe the structure in the special cases where the irreducible components of the exotic Springer fibre have dimension 2, and show that in those cases one obtains Hirzebruch surfaces. Contents

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Components of the Springer fiber and domino tableaux

Cited by 7 publications

References 7 publications

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

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

Topology of two-row Springer fibers for the even orthogonal and symplectic group

Irreducible components of exotic Springer fibres

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