CROSSINGLESS MATCHINGS AND THE COHOMOLOGY OF (n, n) SPRINGER VARIETIES

By Mikhail Khovanov. 2002

89 citations recorded by the source corpus.

In an earlier paper, the author introduced a collection of rings that control a categorification of the quantum sl(2) invariant of tangles. We prove that centers of these rings are isomorphics to the cohomology rings of the (n, n) Springer varieties and show that the braid group action in the derived category of modules over these rings descends to the Springer action of the symmetric group.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0639d189bfedda4a4154540068df8d96acb4fe1c

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Projective-injective modules, Serre functors and symmetric algebras (2005, methodology): “2 we confirm [48], Conjecture 4, concerning the centre of A, and in Theorem 5.”
Buildings, spiders, and geometric Satake (2011, methodology): “This Springer fibre formalism and this description of it have been used as a model of Khovanov homology [22,41].”
Categorification of (induced) cell modules and the rough structure of generalized Verma modules (2007, unknown): “[40,83]).”
An invariant of tangle cobordisms (2002, background): “We investigated the center of H (and not just its degree 0 component) in [8].”
Braid cobordisms, triangulated categories, and flag varieties (2006, background): “These functors, which appeared in [ Kh3 , Proposition 7], satisfy braid relations, and the same argument as in Rouquier [Ro1] implies that the braid group action on the derived category of sheaves on the disjoint union of Ysµ, over all elements s of the symmetric group Sk+1, is genuine.”
A link invariant from the symplectic geometry of nilpotent slices (2004, background): “This was one of Khovanov’s motivations when he proposed that these particular manifolds should be relevant for understanding Kh [15].”
Schur–Weyl duality for higher levels (2006, background): “blocks simultaneously. For this reason, it is important to find some more explicit information about the individual blocks of the degenerate cyclotomic Hecke algebras, especially their centers; see [ Kh , S2] for further motivation for such questions.”