112 problems

Let $M$ be a Calabi–Yau threefold, let $H^*(M)$ denote its cohomology, and let $W^+(M)$ be the algebra generated by $T_n(\lambda)$ for $n{\geqslant} 0$ and $\lambda\in H^*(M)$, sub…

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 $\mathfrak{g}=\mathfrak{sp}_4$, let $f$ be a subregular nilpotent element, and let $k$ be an admissible level. Write $L(\xi^{(s)}_{i,j},\chi^{(s)}_{i,j})$ for the simple…

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 $Z(\mathbf{t})$ be the exponential of the $\mathrm{KdV}_r$ potential function. Let $W_r^+$ denote the relevant algebra of differential operators, containing the Virasoro genera…

Minus-reduction conjecture. For any $\ta{ \kappa}\in\mathbb C$ and any V\in\operatorname{Obj}\ta{ O}_{\ta{ \kappa}},

Global Plücker formula. For each $k$, one has

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…

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

Let $\mathcal{A}$ be a unital C$^*$-algebra. A MASA is a maximal abelian C$^*$-subalgebra of $\mathcal{A}$, and a W$^*$-algebra is a C$^*$-algebra admitting a Banach-space predual.…

Let $G$ be a reductive group with maximal torus $T$, coweight lattice $X_{*}(T)$, dominant coweights $X_{*}(T)_{+}$, Langlands dual group $\check{G}$, and principal equivariant aff…

Let $\mathfrak{g}$ be a simple Lie algebra, let $f$ be a nilpotent element, and set … Let $V_2$ be the weight-two Griess algebra of $V$. Griess-algebra conjecture. The algebra…

Let $X_V$ denote the associated variety of a vertex algebra $V$, and let $\mathbb{O}_{F_4(a_3)}$ be the nilpotent orbit of Bala–Carter type $F_4(a_3)$ in $F_4$. Level $-6$ $F_4$ co…

Three-legs PT3 $qq$-character collision conjecture.

Let $W_k(\mathfrak{g},f)$ be a unitary minimal $W$-algebra, with corresponding conformal net denoted by $\mathcal{A}_{W_k(\mathfrak{g},f)}$. The algebra is strongly rational when i…

Let $W$ be a unital $F$-algebra over a field of characteristic zero, and let $A$ be a $W$-algebra. Say that the action of $W$ on $A$ is finite when the image of the action has fini…

Let $A$ be a $W$-algebra over a field of characteristic zero. A class of algebras has the Specht property if every $T$-ideal of the class is finitely generated. The Specht conjectu…

Let $(a_1,\dots,a_s,a_{s+1},\dots,a_r)$ be a partition of $n$, let $f_2$ be a nilpotent element of $\mathfrak{sl}_n$ corresponding to this partition, and set…

Let $\mathcal{W}^{\mathfrak{sp}}_{\infty}(c,\mathsf{k})$ be the universal two-parameter vertex algebra, let $\mathrm{H}^0_{\ydiagram{2}}$ denote its Virasoro-type reduction, and le…

Let $\mathbb{O}$ be a nilpotent orbit of $\mathfrak{g}$, with representative $f\in\mathfrak{g}$ satisfying … and assume that the nonzero semisimple element of…

Let $\mathfrak{g}$ be $\mathfrak{so}_N$ or $\mathfrak{sp}_N$, and let … be a partition parametrizing a nilpotent orbit, with $m_i\in\{1,2\}$ subject to the parity conditions for th…

Let $\lambda=(\lambda_1\geq\lambda_2\geq\cdots\geq\lambda_\ell)$ be a partition of $N$, and set … Let $\mathrm{H}_{\mathbb{O}_{\widehat{\lambda}_i}}^0$ denote the BRST reduction as…

Let $n$ be the parameter in the families of vertex algebras, and set … Here $f_{\rm pr}$ and $f_{\rm sub}$ denote respectively principal and subregular nilpotent elements. Kazama–S…