# Group partition categories

@article{Likeng2021GroupPC, title={Group partition categories}, author={Samuel Nyobe Likeng and Alistair Savage}, journal={Journal of Combinatorial Algebra}, year={2021} }

To every group $G$ we associate a linear monoidal category $\mathcal{P}\mathit{ar}(G)$ that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of $\mathcal{P}\mathit{ar}(G)$ into the group Heisenberg category associated to $G$. This embedding intertwines the natural actions of both categories on modules for wreath products of $G$. Finally, we prove…

## 2 Citations

### Heisenberg Categorification and Wreath Deligne Category

- Mathematics
- 2020

We define a faithful linear monoidal functor from the partition category, and hence from Deligne’s category Rep(St), to the additive Karoubi envelope of the Heisenberg category. We show that the…

### Multiparameter colored partition category and the product of the reduced Kronecker coefficients

- Mathematics
- 2022

A BSTRACT . We introduce and study a multiparameter colored partition category CPar ( x ) by extending the construction of the partition category, over an algebraically closed ﬁeld 𝕜 of…

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