  In this paper we introduce and study a categorical action of the positive
part of the Heisenberg Lie algebra on categories of modules over rational
Cherednik algebras associated to symmetric groups. We show that the generating
functor for this action is exact. We then produce a categorical Heisenberg
action on the categories $\mathcal{O}$ and show it is the same as one
constructed by Shan and Vasserot. Finally, we reduce modulo a large prime $p$.
We show that the functors constituting the action of the positive half of the
Heisenberg algebra send simple objects to semisimple ones, and we describe
these semisimple objects.
