On the topology of components of some Springer fibers and their relation to Kazhdan¿Lusztig theory
By Francis Y. C. Fung. 2002
106 citations recorded by the source corpus.
Abstract We describe the irreducible components of Springer fibers for hook and two-row nilpotent elements of gl n ( C ) as iterated bundles of flag manifolds and Grassmannians. We then relate the topology (in particular, the intersection homology Poincare polynomials) of the pairwise intersections of these components with the inner products of the Kazhdan–Lusztig basis elements of irreducible representations of the rational Iwahori–Hecke algebra of type A corresponding to the hook and two-row Young shapes.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7170f9091c87790cf83c8e84bb78cd77d9c9c5c4
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Ben Webster
- Megumi Harada
- C. Stroppel
- M. Masuda
- T. Horiguchi
- Hiraku Abe
- Julianna Tymoczko
- Aaron D. Lauda
In Mathematical Physics
- Ben Webster
- Megumi Harada
- C. Stroppel
- M. Masuda
- T. Horiguchi
- Hiraku Abe
- Julianna Tymoczko
- Aaron D. Lauda
Citations in the corpus
- 2-block Springer fibers: convolution algebras and coherent sheaves (2008, background): “We first recall the description of irreducible components of these Springer fibers (following [ Fun03 ]), and more generally consider the closure of cells in the Biaoynicki-Birula paving of the Springer fiber.”
- A positive Monk formula in the S1‐equivariant cohomology of type A Peterson varieties (2009, background): “Hessenberg varieties arise in many areas of mathematics, including geometric representation theory [12, 31, 33], numerical analysis [8], mathematical physics [24, 29], combinatorics [10], and algebraic geometry [5, 6, 34, 35].”
- The cohomology rings of regular nilpotent Hessenberg varieties in Lie type A (2015, background): “This subject lies at the intersection of, and makes connections between, many research areas such as geometric representation theory (see for example [43, 18]), combinatorics (see e.”