4 problems

Let $(d,r)$ denote the degree of a positive root in the proposed BKM superalgebra associated with the second denominator formula. Simple-root conjecture. The only simple roots are…

Let $C_{d,r}(n)$ be the coefficients appearing in the product formula … The signs satisfy $C_{0,0}(n),C_{1,1}(n)\geq0$ and $C_{0,1}(n),C_{1,0}(n)\leq0$. Root-multiplicity conjectur…

Let $\mathfrak g$ be the constructed BKM superalgebra, and consider the quotient of the space of BRST-exact, $Q_L$-closed states by its subspace of $Q_L$-exact states. BRST realiza…

Let $\Delta_k$ denote the three genus-two modular forms labelled by $k=2,1,\frac12$ and studied by Gritsenko and Nikulin. For the type IIB $\mathbb{Z}_n\times\mathbb{Z}_n$ models,…