Embedding Deligne's category \(\underline{\mathrm{Re}}\mathrm{p}(S_t)\) in the Heisenberg category (with an appendix written with Christopher Ryba) (Q2043520)

Summary: 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.