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Jellyfish Partition Categories

  • Jonathan Comes
Article
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Abstract

For each positive integer n, we introduce a monoidal category \(\mathcal {J}\mathcal {P}(n)\) using a generalization of partition diagrams. When the characteristic of the ground field is either 0 or at least n, we show \(\mathcal {J}\mathcal {P}(n)\) is monoidally equivalent to the full subcategory of Rep(An) whose objects are tensor powers of the natural n-dimensional permutation representation of the alternating group An.

Keywords

Jellyfish partition category Partition algebra Alternating group Representation theory 

Mathematics Subject Classification (2010)

16S99 05E99 18D10 

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Notes

Acknowledgements

I would like to thank Jonathan Kujawa for initiating this project by pointing out the paper [6], and for several useful conversations since. Part of this project was completed while I enjoyed a visit to the Max Planck Institute in Bonn. I would like to thank the institute for their hospitality.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.BoiseUSA

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