16 problems

Let $A_{5+1/2}$ denote the intermediate Lie algebra between $A_5$ and $E_6$, and let $L_k(A_{5+1/2})$ be its affine VOA at positive integer level $k$. Write $r(k)$ for the number o…

Let $\mathfrak{g}_I$ be an intermediate Lie algebra between $\mathfrak{g}_1$ and $\mathfrak{g}_2$, and let the associated theta block be constructed from the positive roots and wei…

Let $AD_{3+1/2}$ be the intermediate Lie algebra between $A_1^3$ and $D_4$, and let $L_k(AD_{3+1/2})$ be its affine VOA at positive integer level $k$. Higher-level non-rationality…

Let $L_k(A_{5+1/2})$ be the affine VOA of the intermediate Lie algebra $A_{5+1/2}$ at integer level $k$. Higher-level non-rationality conjecture for $A_{5+1/2}$. The VOA…

Let $L_2(A_{5+1/2})$ be the affine VOA of the intermediate Lie algebra $A_{5+1/2}$ at level $2$, with conformal weights $h_\lambda$ listed with multiplicities indicated by subscrip…

Let $R_\lambda$ be a highest-weight module of one of $E_{7+1/2}$, $D_{6+1/2}$, or $A_{5+1/2}$, let $\rho$ be the Weyl vector, and let $\langle\,\ \rangle_{\mathfrak{g}_{\rm sub}}$…

For each intermediate Lie algebra in the intermediate exceptional series, form the theta block from its associated positive roots and weights, using the construction described in t…

Let $\mathsf{QExc}_{R,v,w}$ be the quantum exceptional diagram category. A trivalent ribbon category is a ribbon category generated by a trivalent vertex, and a ribbon functor pres…

Let $U$ be a subset of $\mathbb C^2$, and let the Cauchy completion denote the additive and idempotent completion. Quantum semisimplicity conjecture. There is an open dense subset…

Let $R$ be a ring and let $\mathsf{QExc}_{R,v,w}$ be the quantum exceptional diagram category, with $\mathbb Q(v,w)$-valued closed-diagram evaluations defined by the stated relatio…

Quantum sufficiency conjecture. If every polynomial in $\mathbf P$ is invertible in $R$, then the space of $n$-boundary-point diagrams in $\mathsf{QExc}_{R,v,w}$ is finitely genera…

Let $\mathsf{Exc}_{R,\lambda}$ be the classical exceptional diagram category. A rigid symmetric monoidal category is a symmetric monoidal category in which every object has a dual,…

Let $U$ be a subset of $\mathbb C$, and let the Cauchy completion mean the additive and idempotent completion of a category. Classical semisimplicity conjecture. There is a dense s…

Let $R$ be a ring and let $\mathsf{Exc}_{R,\lambda}$ be the classical exceptional diagram category, with $\mathsf{Exc}_{R,\lambda}(0)$ its closed-diagram space and the empty diagra…

Let $R$ be a ring and let $\boldsymbol{\lambda}$ be a parameter such that the category $\mathsf{Exc}_{R,\lambda}$ is defined; write $\mathsf{Exc}_{R,\lambda}(n)$ for its space of d…

A symmetric ribbon category is a monoidal category equipped with symmetry and ribbon structure, and a one-parameter family of Lie algebra objects is a family parametrized by a cont…