10 problems

Suppose $\mathscr{P}_{\bullet,\pm}$ is an irreducible subfactor planar algebra. For $x\in\mathscr{P}_{2,\pm}$, let $\mathfrak{F}(x)$ denote its Fourier transform, and let $P,Q$ be…

Eulerian-interval conjecture. If $[e_1,\operatorname{id}]$ is Eulerian, then $\varphi(\mathcal{P})$ is nonzero, and consequently $\mathcal{P}$ is w-cyclic.

Nonvanishing Euler-characteristic conjecture. The Euler characteristic $\chi(\mathcal{P})$ is nonzero.

Distributive biprojection lattice conjecture. Every irreducible subfactor planar algebra with a distributive biprojection lattice is w-cyclic.

Let $G$ be a non-trivial finite group, let $\cR_\bullet$ be the reduced subfactor planar algebra of a $3^G$ subfactor planar algebra, and let $\cQ_\bullet$ be the planar subalgebra…

Let $G$ be a non-trivial finite group, and let a $3^G$ subfactor planar algebra be a subfactor planar algebra whose principal graph is a $3^{|G|}$ spoke graph. Let $\theta$ be the…

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 al…

Let $G$ be a finite group, let $\cP_\bullet$ be a $3^G$ subfactor planar algebra, and for each $g\in G\setminus\{1\}$ let $p_g$ be the projection in $\cP_{4,+}$ corresponding to…

Let $G$ be an abelian group and let a $3^G$ subfactor be a subfactor whose principal graph has the indicated $3^G$ spoke form. Its quantum double is the Drinfeld center of the asso…

W-cyclicity conjecture. Every distributive subfactor planar algebra is w-cyclic.