2012 / June Volume 7 No.2
A Survey Of Heisenberg Categorification via Graphical Calculus
Published Date |
2012 / June
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Title | A Survey Of Heisenberg Categorification via Graphical Calculus |
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Keyword | |
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Pagination | 291-321 |
Abstract | In this expository
paper we present an overview of various graphical categorifications
of the Heisenberg algebra and its Fock space representation. We
begin with a discussion of ``weak'' categorifications via modules
for Hecke algebras and ``geometrizations'' in terms of the
cohomology of the Hilbert scheme of points on the resolution of a
simple singularity. We then turn our attention to more recent
``strong'' categorifications involving planar diagrammatics and
derived categories of coherent sheaves on Hilbert schemes.
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AMS Subject Classification |
20C08, 14F05, 17B65
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Received |
2011-07-14
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Accepted |
2011-07-20
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