A Survey of Heisenberg Categorification via Graphical Calculus
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چکیده
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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تاریخ انتشار 2011