The Categorified Heisenberg Algebra I: A Combinatorial Representation
Jeffrey C. Morton and Jamie Vicary
We give an introductory account of Khovanov's categorification of the Heisenberg algebra, and construct a combinatorial model for it in a 2-category of spans of groupoids. We also treat a categorification of U(sl_n) in a similar way. These give rise to standard representations on vector spaces through a linearization process.