Betti numbers of Springer fibers in type \(A\)

DOI10.1016/j.jalgebra.2009.07.008zbMath1186.14051arXiv0706.3656OpenAlexW2963308107MaRDI QIDQ5902564

Lucas Fresse

Publication date: 8 January 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.3656

zbMATH Keywords

Young diagramsCoxeter lengthflagsSpringer fiberSchubert cells

Mathematics Subject Classification ID

Classical groups (algebro-geometric aspects) (14L35) (Co)homology theory in algebraic geometry (14F99)

Related Items (20)

Generating functions for inverted semistandard Young tableaux and generalized ballot numbers ⋮ Betti numbers of the Springer fibers over nilpotent elements in \(gl_n(\mathbb{C})\) of Jordan form \((2^b,1^{a-b})\) ⋮ Springer fibers and Schubert points ⋮ Euler characteristic of analogues of a Deligne-Lusztig variety for \(\mathrm{GL}_{n}\) ⋮ A notion of inversion number associated to certain quiver flag varieties ⋮ Counting covered fixed points and covered arcs in an involution ⋮ Smooth components of Springer fibers ⋮ Cell decompositions of quiver flag varieties for nilpotent representations of the cyclic quiver ⋮ Unimodality of the distribution of Betti numbers for some Springer fibers ⋮ Hessenberg varieties of parabolic type ⋮ The geometry and combinatorics of Springer fibers ⋮ Combinatorics of tableau inversions ⋮ On the existence of smooth orbital varieties in simple Lie algebras ⋮ A unified approach on Springer fibers in the hook, two-row and two-column cases ⋮ On the singularity of the irreducible components of a Springer fiber in \({\mathfrak{s}\mathfrak{l}_n}\) ⋮ Representation stability of the cohomology of Springer varieties and some combinatorial consequences ⋮ Euler characteristic of Springer fibers ⋮ An equivariant basis for the cohomology of Springer fibers ⋮ Poincaré polynomial at \(-1\) associated with a Young diagram of three rows ⋮ Inversions of semistandard Young tableaux

Cites Work

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• A partition of the Springer fibers \({\mathcal B}_N\) for type \(A_{n-1}\), \(B_2\), \(G_2\) and some applications
• The fixed point subvarieties of unipotent transformations on the flag varieties
• Green polynomials and singularities of unipotent classes
• Classes unipotentes et sous-groupes de Borel
• Trigonometric sums, Green functions of finite groups and representations of Weyl groups
• Homology of moduli spaces of instantons on ALE spaces. I
• Flag varieties and interpretations of Young tableau algorithms
• Some theorems on actions of algebraic groups
• Homology of the Zero-Set of a Nilpotent Vector Field on a Flag Manifold
• On Unipotent and Nilpotent Elements of Groups of Type E ₆
• Lectures on the Geometry of Flag Varieties

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