Categorification of the Heisenberg algebra and MacMahon function

Abstract

Starting from a one dimensional vector space, we construct a categorification $'\mathcal H$ of a deformed Heiserberg algebra $'H$ by Cautis and Licata's method. The Grothendieck ring of $'\mathcal H$ is $'H$. As an application, we discuss some related partition functions related to the MacMahon function of 3D Young diagram. We expect further applications of the results of this paper.

substantial exposition added from the first version, 22 pages