14 problems

Let $K$ be an algebraically closed field of characteristic zero, let $G$ be a finite abelian group, and let … Let $A$ be a finite-dimensional cocommutative cosemisimple Yetter–Drin…

Let $U_0$ be the subspace used in the paper's decomposition associated with a tridiagonal pair, and let $L$ and $R$ denote the corresponding lowering and raising maps. Commutativit…

Finiteness conjecture. In any given dimension, the number of non-isomorphic weak Hopf algebras $H$ with this property is finite.

Let $R$ be a unitary involutive $R$-matrix. An invertible matrix $\alpha$ is assumed to satisfy the relation referred to as Eq. (Ralphadef-graphical), and $\theta$ denotes the part…

Let $\mathcal{C}$ be a modular, ribbon or braided fusion category over $\mathbb{C}$. A category is Hermitian over a field $K$ when it admits the corresponding Hermitian structure d…

Large-$N$ commutation-relation conjecture. In the large $N$ limit, these operators satisfy

Let $p\geq 2$, set $\epsilon_1=1$, $\epsilon_2=k+p$, and define the rescaled operators … Let $\mathcal B$ be an appropriate energy eigenbasis for the Hilbert space. Non-Abelian lar…

Specialization conjecture. Under the algebraic specialization $\wp(x)=x^n$, the groups

Weak-integrality conjecture. These braid group representations have finite image for all $n>0$ if and only if $\operatorname{FPdim}(X)^2\in\mathbb Z$.

Let $R_X:\mathbb C^m\otimes\mathbb C^m\longrightarrow\mathbb C^m\otimes\mathbb C^m$ be a unitary (generalized) $R$-matrix of finite order, used to define braid group representation…

A generalized Yang–Baxter equation object (gYBE object) is an object in a unitary ribbon fusion category that produces braid group representations through the associated $(d,3,1)$-…

Let ${\bf k}$ be an algebraically closed field of characteristic zero, let $\mathbb G_{m,\bf k}^{2n}$ carry the standard symplectic form … and let $BirSympl_{n,\bf k}$ be the group…

Pointedness conjecture. The Hopf algebra $H$ or its dual $H^*$ is pointed.

Quantum spectral conjecture. The displayed formula gives the complete spectrum of the quantum alternating Hilbert matrix, with separate forms according to the parity of $N$. The so…