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A Survey Of Heisenberg Categorification via Graphical Calculus
by Anthony Licata   Alistair Savage

Vol. 7 No. 2 (2012) P.291~P.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.

KEYWORDS
Categorification, Heisenberg algebra, Hecke algebra, planar diagrammatics, Hilbert scheme, Fock space

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20C08, 14F05, 17B65

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