18 problems

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…

Eguchi–Hori–Xiong conjecture. The partition function satisfies

Let $\g$ be one of $\W{-1}$, $W$, or $\Vir$, and let $\Ua(\g)$ be its enveloping algebra. ACC conjecture. The algebra $\Ua(\g)$ satisfies the ascending chain condition on primitive…

Let $\g$ be one of $\W{-1}$, $W$, or $\Vir$, and let $\Ua(\g)$ be its enveloping algebra. Complete-primality conjecture. Every primitive ideal of $\Ua(\g)$ is completely prime. The…

Let $\g$ be one of $\W{-1}$, $W$, or $\Vir$. Let $\operatorname{P.Prim}\operatorname{S}(\g)$ denote the Poisson primitive spectrum of the symmetric algebra and let…

Let $\g$ be one of $\W{-1}$, $W$, or $\Vir$, and let $\chi$ and $\eta$ be local functions on $\g$. Let $P(\chi)$ and $P(\eta)$ denote the associated Poisson primitive ideals, and l…

Let $\g$ be one of $\W{-1}$, $W$, or $\Vir$, and let $\chi$ and $\eta$ be one-point local functions on $\g$. Let $P(\chi)$ and $P(\eta)$ denote their associated Poisson primitive i…

Let $V\!ir$ be the Virasoro algebra, let $z$ denote its central element, and let $\operatorname{U}(V\!ir)$ be its universal enveloping algebra. The Virasoro central-quotient simpli…

Let $\Phi^{\Delta}_{\Lambda,\Lambda}(\alpha,\beta,c_{\emptyset};z)$ be a ramified irregular vertex operator with expansion coefficients $c_{\lambda}^{(m)}$, and let…

Let $p,q$ be positive integers, let … and let $\chi_{p,q}$ be the singular vector of level $pq$ in $M_{\Delta_{p,q}}$. A ramified irregular vertex operator is called singular when…

Let $r$ be a positive integer and let $M^{[r]}_{\Lambda}$ be an irregular Verma module with $\Lambda_{2r-1}\neq 0$ and $\Lambda_{2r}=0$. A ramified irregular vertex operator has an…

Modular GKO conjecture. If $\operatorname{char}{\mathbb F}>2\ell^2+\ell-3$, then the multiplicity-free decomposition above is valid over ${\mathbb F}$ as a direct sum of irreducibl…

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

Let $n,k\in\mathbb{N}$ with $n\geq k$, and let $\mathbf{r}\in\Gamma(n,k)$. Let $V(\mathbf{r})^{\times}$ denote the subset of $V(\mathbf{r})$ consisting of the relevant nonzero solu…

Heisenberg–Virasoro extension. The KW and Hodge tau-functions are related by

Let $\nu_0$ be the probability measure induced by Werner's loop measure on the triangular factorization parameter $a$ of a welding homeomorphism, and let $\beta_0<\frac{5\pi^2}{4}$…

Let $c=c{p,q} eq 0$ and let $L(c,h)$ be a minimal model. Let $V{\alpha,\beta}^{\prime}$ be an irreducible module from the intermediate series, and let an admissible triple mean a…

Mazorchuk's conjecture. There are no irreducible mixed modules over the Virasoro algebra.