Heisenberg categorification and Hilbert schemes

Published 27 Sep 2010 in math.QA and math.AG | (1009.5147v3)

Abstract: Given a finite subgroup G of SL(2,C) we define an additive 2-category H^G whose Grothendieck group is isomorphic to an integral form of the Heisenberg algebra. We construct an action of H^G on derived categories of coherent sheaves on Hilbert schemes of points on the minimal resolutions of C^2/G.

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