23 problems

Rehren's conjecture. The representation category of $\2F$ is non-degenerate.

Let $\2K$ be a pre-modular tensor category. A fully embedded subcategory is one included as a full tensor subcategory of a modular category $\2C$. Write $\2Z_2(\2K)$ for the center…

Let $\2C$ be a braided tensor $C^*$-category of finite dimension, and let $\2Z(\2C)$ denote its center. A modular extension of $\2C$ is a modular category $\2M$ containing $\2C$ as…

Let $\2C_0$ be a finite non-modular braided tensor category, and let $\2Z(\2C_0)$ denote its center. A modular category $\2C$ is an ambient modular category containing $\2C_0$ as a…

Let $l\geq 12$ be divisible by $3$, and let $q$ be the parameter defining $\mathcal{C}(G_2,G_2(a_1),l,q)$. Let $T(\omega_1)$ and $T(\omega_2)$ be the tilting modules of highest wei…

Let $l\geq 7$ be an integer not divisible by $3$, and let $q$ be the parameter defining the braided finite tensor category $\mathcal{C}(G_2,G_2(a_1),l,q)$. Write $T(\omega_1)$ and…

Categorical splitting conjecture. There is an equivalence of braided tensor categories

Let $\mathcal{C}$ be a braided finite tensor category and let $A$ be a commutative algebra in $\mathcal{C}$. Let $\mathcal{C}_A$ be the category of left $A$-modules, and let…

For each $d\in\mathbb{Z}_{\geq 0}$, let $Q(d)$ be the factorizable quasi-Hopf algebra introduced in the cited work, and let $SF^+_d$ denote the even part of the symplectic fermion…

Let $cmathfrak{g}$ be a complex finite-dimensional simple Lie algebra, let $cell$ be a positive integer, and let $czeta$ be an allowed root of unity defining the modular functor…

Let $V$ be one of the vertex algebras specified by the paper's extension pairs, let $A$ be the corresponding free field algebra, and let $\mathfrak{N}$ be the Nichols algebra gener…

Let $\mathscr{V}$ be a possibly non-semisimple modular tensor category and let $\mathcal{V}=\operatorname{Ind}(\mathscr{V})$. The unit inclusion induces a relative theory, while…

Let $\mathscr{E}$ be the vertex tensor category of $W^0_{\!A_2}(2)$-modules obtained by decomposing the relevant $L_{-\frac{3}{2}}(\mathfrak{sl}_3)$-modules, and let…

Quantum group–singlet correspondence conjecture. The category of weight modules of $\overline{U}_q^H(\mathfrak{sl}_{2})$ is braided equivalent to that category of $\mathcal{M}(p)$-…

Aganagic–Frenkel–Okounkov conjecture. W-algebra modules and Weyl modules of the affine vertex operator algebra should be related by a braided equivalence whenever the displayed rel…

Skein-theoretic cobordism conjecture. We further conjecture that $F_M$ is given on $X$ and $Y$ by

Let $\mathfrak g$ be a simple Lie algebra, with dual Coxeter number $h^\vee$ and lacety $d$. Let $\ell=-h^\vee+\frac{a}{b}$ be an admissible level, where $a,b$ are coprime positive…

Let $\mathfrak g$ be a simple Lie algebra, with dual Coxeter number $h^\vee$ and lacety $d$. Let $\ell=-h^\vee+\frac{a}{b}$ be an admissible level, where $a,b$ are coprime positive…

Let $G$ be the group associated with $\mathfrak{g}$, let $\operatorname{Gr}_G$ be its affine Grassmannian, and let $\operatorname{Whit}^c(\operatorname{Gr}_G)$ denote the Whittaker…

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra, let ${}^L\mathfrak{g}$ be its Langlands dual, and let $\widehat{{}^L\mathfrak{g}}_{{}^Lk}\text{-mod}^0$ and…

Temperley–Lieb–Virasoro braided equivalence conjecture. There is an equivalence of braided tensor categories

Let $\mathcal{C}$ be the braided finite tensor category under consideration, let $\Omega_{\mathcal{C}}$ be the matrix associated with the pairing in Equation, and let…

Feigin–Gainutdinov–Semikhatov–Tipunin conjecture. The braided finite tensor category of grading-restricted generalized modules for a triplet $\mathcal{W}$-algebra should be equival…