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arXiv · 1507.04794

The generator conjecture for $3^G$ subfactor planar algebras

Zhengwei Liu·David Penneys
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Abstract

We state a conjecture for the formulas of the depth 4 low-weight rotational eigenvectors and their corresponding eigenvalues for the $3^G$ subfactor planar algebras. We prove the conjecture in the case when $|G|$ is odd. To do so, we find an action of $G$ on the reduced subfactor planar algebra at $f^{(2)}$, which is obtained from shading the planar algebra of the even half. We also show that this reduced subfactor planar algebra is a Yang-Baxter planar algebra.

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Zhengwei Liu, David Penneys. 2015-07-16. The generator conjecture for $3^G$ subfactor planar algebras. https://arxiv.org/abs/1507.04794

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