17 problems

Let $U_{q,p}(\widehat{\mathfrak{sl}_2})$ be the elliptic algebra introduced in the paper, with screening currents and representation spaces as constructed there. The q-deformed ext…

Admissible monomial basis conjecture. For $1\leq r\leq p-1$, the set of admissible monomials of the form defined in the source, where $r_L=r$, $r_0=1$, and $s=1$, is a basis of…

Monomial basis conjecture. In the general case $p<p'$, the monomials satisfying the quadratic exclusion condition

Eguchi–Hori–Xiong conjecture. All genus-$g$ Gromov–Witten invariants and their descendents for $g\geq 1$ can be uniquely determined by solving recursively the linear system of Vira…

Let ${\cal B}$ be a nontrivial local extension of the $c=1$ Virasoro net ${\cal A}_{(\rm Vir,1)}$. The spectrum condition is that the representation of ${\cal A}_{(\rm Vir,1)}$ on…

General Lie $h$ relations conjecture. The general Lie $h$ relations in $$ are similarly true independent of unitarity.

Let $\mathbb{F}$ be a field of characteristic $p>2$, let $c\in\mathbb{F}$, and let $L_{\operatorname{Vir}}(c,0)_{\mathbb{F}}$ denote the simple quotient Virasoro vertex operator al…

Let $\mathbb{F}$ be a field of characteristic $p>2$, let $c\in\mathbb{F}$, and let $L_{\operatorname{Vir}}(c,0)_{\mathbb{F}}$ denote the simple quotient Virasoro vertex operator al…

Virasoro ground-state construction conjecture. A construction similar to this exists for all levels $\ell\geq3$, and for every such level the infinite set of Virasoro ground states…

Let $\boldsymbol{\tau}$ denote the operator introduced for level … and higher, consider the level-$\ell$ sectors and their maximal and Virasoro ground states. Higher-level operator…

Let $p,q\geq 2$ be coprime integers, let $c_{p,q}=1-\frac{6(p-q)^2}{pq}$, and let $L_{c_{p,q}}$ be the simple Virasoro vertex operator algebra at central charge $c_{p,q}$. Feigin–F…

Let $M$ be a semisimple Frobenius manifold, let its principal hierarchy have tau function $Z_M$, and let $L_m$ be the operators defining the Virasoro symmetries by … A super tau-co…

Let $\operatorname{Vir}_{3,4}$ denote the Virasoro minimal model with parameters $(p,p')=(3,4)$, let $C_{E_8}$ be the Cartan matrix of type $E_8$, and write…

Let $\mathfrak V$ be the three-point Virasoro algebra, let $\hat{\mathfrak g}$ denote the affine current algebra used in the free-field realization, and let $\mathcal F$ be the cho…

Let $R=\mathbb C[t^{\pm 1},u\mid u^2=t^2+4t]$, let $\mathfrak V$ be the three-point Virasoro algebra, and let the three-point current algebra act in the free-field realization on a…

A model of conformal field theory is assumed to be translation and scale invariant when it is invariant under translations and scalings, and it is Möbius invariant when it is invar…

Halpern's orbifold Virasoro conjecture. The extended physical-state conditions should be