2-block Springer fibers: convolution algebras and coherent sheaves
By C. Stroppel, Ben Webster. 2008
73 citations recorded by the source corpus.
For a fixed 2-block Springer fiber, we describe the structure of its irreducible components and their relation to the Bialynicki-Birula paving, following work of Fung. That is, we consider the space of complete flags in C^n preserved by a fixed nilpotent matrix with 2 Jordan blocks, and study the action of diagonal matrices commuting with our fixed nilpotent. In particular, we describe the structure of each component, its set of torus fixed points, and prove a conjecture of Fung describing the intersection of any pair. Then we define a convolution algebra structure on the direct sum of the cohomologies of pairwise intersections of irreducible components and closures of C^*-attracting sets (that is, Bialynicki-Birula cells), and show this is isomorphic to a generalization of the arc algebra of Khovanov defined by the first author. We investigate the connection of this algebra to Cautis & Kamnitzer's recent work on link homology via coherent sheaves and suggest directions for future research.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/633f5b97a384369bcc1c8e52fabbaf26e5ef207c
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Khovanov homology from Floer cohomology (2015, background): “A helpful model of the combinatorial arc algebra for our purposes is that given by Stroppel and Webster [54]: they set Hn = ⊕℘,℘′H ∗(L̂℘ ∩ L̂℘′) and define a modified convolution product on these groups, which (they prove) co-incides with Khovanov’s original TQFT product.”