On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory.
From MaRDI portal
Publication:1408803
DOI10.1016/S0001-8708(02)00072-5zbMath1035.20004arXivmath/0204224MaRDI QIDQ1408803
Publication date: 25 September 2003
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0204224
general linear groupsGrassmanniansflag manifoldshooksYoung diagramsintersection homologyKazhdan-Lusztig theorynilpotent linear mapsSpringer fibrestype \(A\) Hecke algebras
Hecke algebras and their representations (20C08) Representation theory for linear algebraic groups (20G05) Cohomology theory for linear algebraic groups (20G10)
Related Items
A GRAPHICAL CALCULUS FOR 2-BLOCK SPALTENSTEIN VARIETIES ⋮ James' conjecture for Hecke algebras of exceptional type. I. ⋮ Springer fibers and Schubert points ⋮ Intersection theory of the Peterson variety and certain singularities of Schubert varieties ⋮ Hessenberg varieties associated to ad-nilpotent ideals ⋮ Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies ⋮ Upper triangular parts of conjugacy classes of nilpotent matrices with finite number of \(B\)-orbits ⋮ The components of the singular locus of a component of a Springer fiber over \(x^2 = 0\) ⋮ Exotic Springer fibers for orbits corresponding to one-row bipartitions ⋮ RNA, local moves on plane trees, and transpositions on tableaux ⋮ A web basis of invariant polynomials from noncrossing partitions ⋮ Two-row \(W\)-graphs in affine type \(A\) ⋮ Components of Springer fibers associated to closed orbits for the symmetric pairs \((Sp(2n), GL(n))\) and \((O(n), O(p) \times O(q))\). II ⋮ Stratification of a singular component of a Springer fiber over \(x^2 = 0\) of the simplest type ⋮ Smooth components of Springer fibers ⋮ B-orbits of square zero in nilradical of the symplectic algebra ⋮ A simple bijection between standard \(3\times n\) tableaux and irreducible webs for \(\mathfrak{sl}_{3}\) ⋮ Springer fibers and the Delta Conjecture at \(t = 0\) ⋮ An explicit bijection between semistandard tableaux and non-elliptic \(sl _{3}\) webs ⋮ Poset pinball, the dimension pair algorithm, and type \(A\) regular nilpotent Hessenberg varieties ⋮ Hessenberg varieties of parabolic type ⋮ The geometry and combinatorics of Springer fibers ⋮ Springer representations on the Khovanov Springer varieties ⋮ Singular components of Springer fibers in the two-column case ⋮ Singular components of Springer fibers in the two-column case ⋮ A study of irreducible components of Springer fibers using quiver varieties ⋮ Springer fibers for the minimal and the minimal special nilpotent orbits ⋮ On intersections of orbital varieties and components of Springer fiber ⋮ A unified approach on Springer fibers in the hook, two-row and two-column cases ⋮ A categorification of integral Specht modules ⋮ On the singularity of the irreducible components of a Springer fiber in \({\mathfrak{s}\mathfrak{l}_n}\) ⋮ Reducibility of the intersections of components of a Springer fiber ⋮ Irreducible components of two-row Springer fibers for all classical types ⋮ Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology ⋮ Euler characteristic of Springer fibers ⋮ Some characterizations of singular components of Springer fibers in the two-column case ⋮ Springer fiber components in the two columns case for types A and D are normal ⋮ An equivariant basis for the cohomology of Springer fibers ⋮ On the structure of smooth components of Springer fibers ⋮ Ordered set partitions, Garsia-Procesi modules, and rank varieties ⋮ Real Springer fibers and odd arc algebras ⋮ The Cohomology Rings of Regular Nilpotent Hessenberg Varieties in Lie Type A ⋮ Topology of two-row Springer fibers for the even orthogonal and symplectic group ⋮ Transitioning between tableaux and spider bases for Specht modules
Cites Work
- Intersection homology. II
- On Joseph's construction of Weyl group representations
- Relations between Young's natural and the Kazhdan-Lusztig representations of \(S_ n\)
- Intersection homology theory
- Representations of Coxeter groups and Hecke algebras
- Nilpotent orbits, primitive ideals, and characteristic classes. A geometric perspective in ring theory
- Trigonometric sums, Green functions of finite groups and representations of Weyl groups
- Geometric construction of crystal bases
- The representations of Hecke algebras of type \(A_ n\)
- The representation theory of the Temperley-Lieb algebras
- Cellular algebras
- Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs
- Some Intersection Properties of the Fibres of Springer's Resolution
- Representations of Hecke Algebras of General Linear Groups
- Irreducible Components of Fixed Point Subvarieties of Flag Varieties
- Computational Construction of W-graphs of Heeke algebras H(q, n) for nup to 15
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item