Title: Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification,
Abstract: We associate a monoidal category $\mathcal{H}^\lambda$ to each dominant
integral weight $\lambda$ of $\widehat{\mathfrak{sl}}_p$ or
$\mathfrak{sl}_\infty$. These categories, defined in terms of planar diagrams,
act naturally on categories of modules for the degenerate cyclotomic Hecke
algebras associated to $\lambda$. We show that, in the $\mathfrak{sl}_\infty$
case, the level $d$ Heisenberg algebra embeds into the Grothendieck ring of
$\mathcal{H}^\lambda$, where $d$ is the level of $\lambda$. The categories
$\mathcal{H}^\lambda$ can be viewed as a graphical calculus describing
induction and restriction functors between categories of modules for degenerate
cyclotomic Hecke algebras, together with their natural transformations. As an
application of this tool, we prove a new result concerning centralizers for
degenerate cyclotomic Hecke algebras.