We define a faithful linear monoidal functor from the partition category, and hence from Deligne’s category , 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.
Cite this article
Samuel Nybobe Likeng, Alistair Savage, Embedding Deligne's category in the Heisenberg category (with an appendix by Samuel Nyobe Likeng, Alistair Savage and Christopher Ryba). Quantum Topol. 12 (2021), no. 2, pp. 211–242DOI 10.4171/QT/147