Crossingless matchings and the cohomology of (n,n) Springer varieties
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Crossingless matchings and the cohomology of (n,n) Springer varieties

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https://arxiv.org/pdf/math/0202110.pdf
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Abstract

The sequence of rings $H^n, n\ge 0,$ introduced in math.QA/0103190, controls categorification of the quantum sl(2) invariant of tangles. We prove that the center of $H^n$ is isomorphic to the cohomology ring of the (n,n) Springer variety and show that the braid group action in the derived category of $H^n$-modules descends to the Springer action of the symmetric group.

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