Yang–Baxter presentation conjecture for reduced $3^G$ subfactor planar algebras

Let $G$ be a non-trivial finite group, let $\cP_\bullet$ be a $3^G$ subfactor planar algebra, and let $\cR_\bullet$ be its reduced subfactor planar algebra. A Yang–Baxter planar algebra is a planar algebra generated by Yang–Baxter generators subject to the corresponding skein relations. Yang–Baxter presentation conjecture. $\cR_\bullet$ is a Yang–Baxter planar algebra with $|G|-1$ generators.

The authors state that this gives a new skein-theoretic approach to constructing $\cR_\bullet$ and prove the assertion when $|G|$ is odd. The general case remains open in the source.