English

Embedding Deligne's category $\mathrm{\underline{Re}p}(S_t)$ in the Heisenberg category

Representation Theory 2021-11-12 v2 Category Theory

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 Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.

Keywords

Cite

@article{arxiv.1905.05620,
  title  = {Embedding Deligne's category $\mathrm{\underline{Re}p}(S_t)$ in the Heisenberg category},
  author = {Samuel Nyobe Likeng and Alistair Savage and appendix with Christopher Ryba},
  journal= {arXiv preprint arXiv:1905.05620},
  year   = {2021}
}

Comments

23 pages; v2: minor corrections, published version