6 problems

Let $L$ be an even, self-dual lattice of signature $(p,q)$ with $p,q>1$. A system of simple roots for $L$ means a set of lattice roots serving as fundamental roots for the associat…

Let $\sigma$ be the automorphism under consideration, let $Co_0$ denote the automorphism group of the Leech lattice, and let the two types refer to the two types of norm $8$ vector…

For $g\in\mathrm{Co}_0$, let the twisted fake monster algebra be the generalized Kac–Moody superalgebra obtained by twisting the fake monster algebra by $g$. Let $V$ be a suitable…

Let $g$ be an automorphism used to twist the fake monster algebra, and let its twisted denominator function be the associated denominator function. An automorphic form has singular…

A generalized Kac–Moody algebra $\mathfrak{g}$ whose denominator $\Phi_\mathfrak{g}$ is a singular Borcherds product is expected to arise from the BRST cohomology of a suitable ver…

Let a nice generalized Kac–Moody algebra mean an algebra in the class referred to as “nice” in the source. Let the fake Monster Lie algebra and the Monster Lie algebra be the two d…