4 problems

Let $V_L$ be a lattice vertex operator algebra, and let a parabolic-type subVOA mean a subVOA of the parabolic type considered in the paper. Cofiniteness conjecture. All parabolic-…

Let $L$ be an even lattice with bilinear form $\langle\,\ \rangle:L\times L\rightarrow\mathbb{Z}$, let $V_L$ be the corresponding lattice vertex operator algebra, and set $A=L^*/L$…

Let $Lambda$ be a fractional lattice with short basis $alpha_i^{short}$, and let $Lambda^{long}$ be the integral sublattice with associated long basis $alpha_i^{long}$, chosen so t…

Lam–Shimakura conjecture. Every Ising vector of $V_L^+$ belongs to a subVOA $V_U^+$, where $U$ is a sublattice of $L$ isomorphic to $\sqrt{2}A_1$ or $\sqrt{2}E_8$.