128 problems

Let $V$ be a finitely strongly generated, self-dual, quasi-lisse vertex operator algebra of CFT type, and let $\mathcal{C}_V^{\mathrm{ord}}$ denote its category of ordinary modules…

Let $k\in\mathbb Z$ with $k\geq -1$, define … and let $L(x,y)$ denote the irreducible highest-weight $\mathcal W_k$-module with highest weight $(x,y)$. Classification conjecture. T…

Conjecture on $L_{k_m}(D_4)$. For each $m\geq1$, $L_{k_m}(D_4)$ is a quasi-lisse vertex algebra, it has a unique irreducible ordinary module, and $KL_{k_m}(D_4)$ is a semisimple br…

Braided tensor equivalence conjecture. The functor $H_f^0$ is an equivalence of braided tensor categories. The source already states that this functor is an equivalence of abelian…

For $n\geq2$ and $m\geq3$, let $\mathcal F_k(n)$ denote the simple quotient of the symplectic minimal coset family, and let…

Cohomological complete-reducibility conjecture. If every left $V$-module of finite length is completely reducible, then

Let $\mathcal{T}$ be a four-dimensional $N=2$ superconformal field theory, let $\Phi(\mathcal{T})$ be its associated vertex algebra, and let $Higgs_{\mathcal{T}}$ denote its Higgs…

Let $\mathfrak g$ be the Lie superalgebra under consideration, let $k$ lie in its unitarity range, and set … to be the subcategory of weight $W_k^{\min}(\mathfrak g)$-modules with…

Let $\mathfrak{g}$ be a semisimple Lie algebra, let $k\in\mathbf{C}$, and let $f_1,f_2$ be nilpotent elements satisfying the hypotheses of the source's Main Theorem on freeness. Le…

Let $k$ be one of the four levels … The vertex algebra under consideration is the exceptional W-algebra associated with the subregular nilpotent element $f_{subreg}$ of…

Let $n\geq 2$ and let $\mathcal F^k(n)$ be the universal vertex algebra considered in the paper. A truncation curve in the $(c,\lambda)$-plane is parametrized by … … where … … … Le…

Let $W_{1+\infty,-N}$ be the vertex algebra at central charge $-N$, let $\mathfrak h$ be the parameter space used to construct the modules $V(\lambda,-N)$, and let $V(\lambda,-N)$…

MSV sheaf conjecture. For every variety $X$ with only Gorenstein toroidal singularities, there exists a local sheaf $\mathcal{MSV}(X)$ locally isomorphic to the product of…

Master Family degeneration conjecture. Vertex algebras arising from Mirror Symmetry for hypersurfaces defined by $\Delta$ and $\Delta^*$ are degenerations of the Master Family of v…

Lian–Zuckerman's lifting conjecture. The product and bracket extend to a $G_\infty$ structure on $V$. The conjecture is presented as an open problem in the source, with no resoluti…

Let $A_{(m)}(n)$ be the subalgebra generated by $\xi_0,\ldots,\xi_{n-1}$ in $A_{(m)}$, and let $I_{(m)}(n)$ be its defining ideal. For a family…

Griess algebra realization conjecture. There is an OZ vertex algebra $V$ such that

Let $N\geq 1$, and let $V(\Delta)$ be the boundary hypertoric vertex operator superalgebra for the minimal nilpotent orbit closure of $\mathfrak{sl}_N$. Weight conjecture. After re…

Let $n,r,s$ be non-negative integers, and let ${\mathcal C}^{\psi}_{{\mathcal N}=2}(n,r|s)$ denote the corresponding N=2 coset vertex algebra. Procházka–Rapčák duality conjecture.…

Let $n,r,s$ be non-negative integers, and define … Let ${\mathcal C}^{\psi}_{{\mathcal N}=2}(n,r|s)$ be the corresponding coset vertex algebra. Minimal strong generating type conje…

Let $r$ and $m$ be the parameters of a superelliptic algebra, and set … Let $\mathfrak{g}$ be the underlying Lie algebra, let $h^{\vee}$ be its dual Coxeter number, and let $f$ be…

Let $\mathcal{V}$ be a vertex algebra, let $\mathfrak{Z}_{\mathcal{M}_1},\ldots,\mathfrak{Z}_{\mathcal{M}_n}$ be screening operators, and let $\mathcal{W}\subset\mathcal{V}$ be the…

Assume $n\geqslant m$, with $\kappa_c$ the critical level, and let $\mathfrak{z}$ denote the commutative center. Let $\mathcal{A}^m_{\mathrm{deg}}$ be the degenerate $\beta\gamma$-…

Assume $n\geqslant m$, and let $\kappa_c$ denote the critical level. Let $\mathcal{A}^m_{\mathrm{deg}}$ be the degenerate $\beta\gamma$-system associated with…

Ito's conjecture. There is an isomorphism of vertex superalgebras