14 problems

Read–Rezayi conjecture. The Jones representation of the braid groups at an $r$-th root of unity describes the non-abelian statistics of fractional quantum Hall liquids at filling f…

Parton basis conjecture. These basis elements are parton-like; equivalently, they are products of $M$ Slater determinants.

Parton decomposition conjecture. Every such polynomial can be written as

Parton spanning conjecture. Parton-like states generally span this subspace for any given number of Landau levels.

Let $k$ and $\rho$ be parameters defining the negative rational $(k,\rho)$-admissible Jack polynomials, and let $\mathrm{WA}_{k-1}(k+1,k+\rho)$ denote the corresponding minimal mod…

Predominant orientation-type conjecture. The partition $\Lambda(n,v,d)$ is predominant among all non-vanishing orientation types of $G$.

Squeezing conjecture. Any root partition of $P_G$ can be squeezed into $\Lambda(n,v,d)$.

Predominance conjecture. The partition $\Lambda(n,v,d)$ is predominant.

Bernevig–Haldane clustering conjecture. The sequence of specialized Jack polynomials

Let $(\frac{m}{n};S_2,\ldots,S_n)$ be a pattern of zeros, where the parameters satisfy the concave, cluster, parity, and other conditions described immediately beforehand. Classifi…

Let $m$ be the Laughlin parameter, and let $\xi,\xi'$ be fixed complex quasi-hole positions. For the normalized one- and two-quasi-hole wave functions, write $N(\xi,\xi^*)$ and…

Read–Rezayi Abelian quasihole tunneling conjecture. The tunneling amplitude is

Non-Abelian Moore–Read tunneling conjecture. The tunneling amplitude is

Nayak–Wilczek conjecture. The elementary exchange matrices can be interpreted as $\pi/2$ rotations from $\operatorname{SO}(2n)$; equivalently, they can be expressed in terms of the…