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

MILESTONES

Received: 2011-05-09
Revised : 2011-07-14
Accepted: 2011-07-20

Download Full Content