Heisenberg categorification and Hilbert schemes

Sabin Cautis; Anthony Licata

doi:10.1215/00127094-1812726

Heisenberg categorification and Hilbert schemes

Sabin Cautis^*, Anthony Licata

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

51 Citations (Scopus)

Abstract

Given a finite subgroup Γ ⊂ SL₂(C) we define an additive 2-category H_Γ whose Grothendieck group is isomorphic to an integral form H_Γ of the Heisenberg algebra. We construct an action of H_Γ on derived categories of coherent sheaves on Hilbert schemes of points on the minimal resolutions C²/Γ.

Original language	English
Pages (from-to)	2469-2547
Number of pages	79
Journal	Duke Mathematical Journal
Volume	161
Issue number	13
DOIs	https://doi.org/10.1215/00127094-1812726
Publication status	Published - 2012
Externally published	Yes

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title = "Heisenberg categorification and Hilbert schemes",

abstract = "Given a finite subgroup Γ ⊂ SL2(C) we define an additive 2-category HΓ whose Grothendieck group is isomorphic to an integral form HΓ of the Heisenberg algebra. We construct an action of HΓ on derived categories of coherent sheaves on Hilbert schemes of points on the minimal resolutions C2/Γ.",

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AB - Given a finite subgroup Γ ⊂ SL2(C) we define an additive 2-category HΓ whose Grothendieck group is isomorphic to an integral form HΓ of the Heisenberg algebra. We construct an action of HΓ on derived categories of coherent sheaves on Hilbert schemes of points on the minimal resolutions C2/Γ.

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JO - Duke Mathematical Journal

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Heisenberg categorification and Hilbert schemes

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