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

Mathematics – Quantum Algebra

Scientific paper

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20 pages, 7 figures

Scientific paper

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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