9 problems

The even part of the Haagerup subfactor planar algebra $H\mathcal{P}$ is a subfactor planar algebra lying in a one-parameter family of subfactor planar algebras. Haagerup family co…

Paley type $II$ Temperley–Lieb conjecture. Paley type $II$ Hadamard matrix subfactors have Temperley–Lieb standard invariants.

Let $\cP_\bullet$ be a unitary 2-shaded planar algebra. A finite-index homogeneous connected $\rm II_1$ multifactor inclusion is an inclusion $A\subset B$ with finite Jones index a…

Let $N\subseteq M$ be an irreducible subfactor with finite index, and let the number of minimal intermediate subfactors be counted over the inclusion $N\subseteq M$. Polynomial-gro…

Enumeration conjecture. At index $3+\sqrt{5}$, there are exactly $13$ non-Temperley–Lieb subfactor planar algebras: the Bisch–Jones Fuss–Catalan $A_3*A_4$ subfactor planar algebra…

Morrison–Peters conjecture. There are exactly $2$ non-Temperley–Lieb subfactor planar algebras with index in $(5,3+\sqrt{5})$: the unique $\mathfrak{su}(2)_5$ subfactor planar alge…

Let a subfactor planar algebra mean the planar algebra associated with a finite-index subfactor, and let $A_\infty$ denote the infinite-depth principal graph. Consider irreducible…

Suppose that ${\cal A}\subset {\cal B}$ are conformal subnets with finite index. Let the vacuum representation of ${\cal B}$ carry the action of ${\cal A}$, and let $V$ be the spac…

Let $N\subset M$ be an irreducible subfactor, meaning that $N'\cap M=\mathbb{C}$, with finite index. Let $M\subset M_1$ be the Jones basic construction, so that $N'\cap M_1$ is the…