JournalsqtVol. 12, No. 2pp. 211–242

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

  • Samuel Nybobe Likeng

    University of Ottawa, Canada
  • Alistair Savage

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

We define a faithful linear monoidal functor from the partition category, and hence from Deligne’s category Rep(St)\mathrm{\underline{Re}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.

Cite this article

Samuel Nybobe Likeng, Alistair Savage, Embedding Deligne's category Rep(St)\mathrm{\underline{Re}p}(S_t) in the Heisenberg category (with an appendix by Samuel Nyobe Likeng, Alistair Savage and Christopher Ryba). Quantum Topol. 12 (2021), no. 2, pp. 211–242

DOI 10.4171/QT/147