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arXiv · 2601.09003

A Well-Defined Jellyfish Algorithm for the Affine $E_7$ Subfactor Planar Algebra

Melody Molander
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Abstract

In this paper, we contribute to the Kuperberg program by giving a diagrammatic presentation of generators and relations for the affine $E_7$ unshaded subfactor planar algebra. Using this presentation, we prove that its jellyfish algorithm is a well-defined surjection onto $\mathbb{C}$. In particular, this shows that the jellyfish algorithm is an invariant on closed diagrams for this planar algebra.

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BibTeXRIS

Melody Molander. 2026-01-13. A Well-Defined Jellyfish Algorithm for the Affine $E_7$ Subfactor Planar Algebra. https://doi.org/10.1016/j.jpaa.2026.108383

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