The Categorified Heisenberg Algebra I: A Combinatorial Representation

Understand

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.