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

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

arXiv comment23 pages; v2: minor corrections, published version

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Cited by in corpus (1)

• A new approach to the representation theory of the partition category