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

“…As a consequence, we deduce the rectangular symmetry for classical groups. The symmetry provides a natural home for the recent results of [HL14,W15] on the interactions of two-row Slodowy slices of symplectic and orthogonal groups. We also briefly discuss a geometric version of Kraft-Procesi's column-removal and row-removal reductions for classical groups in [KP82,Proposition 13.5].…”

Section: Example Ii: Partial Resolutions Of Nilpotent Slodowy Slicesmentioning

confidence: 99%

Quiver varieties and symmetric pairs

2019

Represent. Theory

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We study fixed-point loci of Nakajima varieties under symplectomorphisms and their anti-symplectic cousins, which are compositions of a diagram isomorphism, a reflection functor and a transpose defined by certain bilinear forms. These subvarieties provide a natural home for geometric representation theory of symmetric pairs. In particular, the cohomology of a Steinberg-type variety of the symplectic fixed-point subvarieties is conjecturally related to the universal enveloping algebra of the subalgebra in a symmetric pair. The latter symplectic subvarieties are further used to construct geometrically an action of a twisted Yangian on torus equivariant cohomology of Nakajima varieties. In type A case, these subvarieties provide a quiver model for partial Springer resolutions of nilpotent Slodowy slices of classical groups and associated symmetric spaces, which leads to a rectangular symmetry and a refinement of Kraft-Procesi row/column removal reductions.

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“…In particular, the center of our algebras D k can be identified with the cohomology ring of some type D Springer fiber, see [6,39] for an analogous result in type A. For a detailed analysis of the corresponding cup diagram combinatorics and the folding procedure in terms of Springer theory, we refer to [40].…”

Section: Hermitian Symmetric Pairsmentioning

confidence: 99%

“…In [14], see also [40], the case = p k is studied from a geometric point of view. Weights λ, μ are identified with fixed point of the natural C * -action on the (topological) Springer fiber of type D k for the principal nilpotent of type A k−1 , and the cup diagrams λ, μ are canonically identified with the cohomology of the closure of the corresponding attracting cells A λ , A μ .…”

Section: Remark 47mentioning

confidence: 99%

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Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians

Ehrig

Stroppel

2016

Sel. Math. New Ser.

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For each integer k ≥ 4, we describe diagrammatically a positively graded Koszul algebra D k such that the category of finite dimensional D k -modules is equivalent to the category of perverse sheaves on the isotropic Grassmannian of type D k or B k−1 , constructible with respect to the Schubert stratification. The algebra is obtained by a (non-trivial) "folding" procedure from a generalized Khovanov arc algebra. Properties such as graded cellularity and explicit closed formulas for graded decomposition numbers are established by elementary tools.Mathematics Subject Classification 05E10 · 14M15 · 17B10 · 17B45 · 55N91 · 20C08

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

Cited by 15 publications

References 20 publications

Euler Characteristic of Springer Fibers

Euler Characteristic of Springer Fibers

Quiver varieties and symmetric pairs

Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians

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