Crossingless matchings and the cohomology of (n,n) Springer varieties
Mikhail Khovanov
Abstract
The sequence of rings Hn, n 0, introduced in math.QA/0103190, controls categorification of the quantum sl(2) invariant of tangles. We prove that the center of Hn is isomorphic to the cohomology ring of the (n,n) Springer variety and show that the braid group action in the derived category of Hn-modules descends to the Springer action of the symmetric group.
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