Embedding Deligne's category $\underline{\mathrm{Re}}\mathrm{p}(S_t)$ in the Heisenberg category (with an appendix by Samuel Nyobe Likeng, Alistair Savage and Christopher Ryba)

Abstract

We define a faithful linear monoidal functor from the partition category, and hence from Deligne’s category $\underline{\mathrm{Re}}\mathrm{p}(S_t)$, to the additive Karoubi envelope of the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.