13 problems

Statistical interaction matrix conjecture. The matrix $\mathbf{G}_4$ above, together with these three universal chiral partition functions, describes (up to equivalence) one untwis…

Statistical interaction matrix conjecture. The exclusion statistics of the intertwiners in $\operatorname{PF}_2(\mathfrak{sl}_3)$ are encoded by the matrix $\mathbf{G}_3$ above. Th…

For each integer $n\geq1$, let ${\mathcal D}^k(n)$ be the generalized orthogonal parafermion algebra defined by … Suppose ${\mathcal D}^k(n)$ is of type…

Let $p$geq$1$, let $M$ be the chain length, and let $\overline M=M/(p+1)$ denote the number of quasi-particle quantum numbers $\mathfrak{p}_k$. For $p=1$, these quantum numbers are…

Algorithmic conjecture. The method is an algorithm for finding zero modes to any order in perturbation theory.

$\mathcal{W}B_3(7,9)$ conjecture. The critical theory of the anyon chain is the $\mathcal{W}B_3(7,9)$ rational conformal field theory, with the same central charge and conformal we…

SLE conjecture. The curve $\gamma$ has the statistics of

SLE conjecture. The curve created by inserting parafermionic operators at two boundary points has the law

Parafermion conjecture. For general $p$, $\mathbb{C}_{\mathfrak{q}}[z,\partial]$ should allow expressing the relations among the fields of the $(p,1)$ model with an explicit quantu…

Inhomogeneous Baxter-lattice FZ conjecture. These values give the location of the FZ points in the inhomogeneous model.

Anisotropic triangular-lattice FZ conjecture. The conditions

Discretely holomorphic spinor conjecture. For $1\leq m\leq [N/2]$, the variables

Fateev–Zamolodchikov point conjecture. There are $n<\frac12N$ points in the phase diagram corresponding to FZ parafermionic models of the first kind.