5 problems

Let $V$ be a simple, strongly regular vertex operator algebra, and let $\frak h$ be a nondegenerate abelian Lie subalgebra of $V_1$. A positive-definite even lattice is a lattice w…

Let $P$ and $Q$ be the weight and root lattices, let $P^+$ be the dominant weights, and choose complex parameters $\Psi$ and $\Psi'$ as in the affine extension construction. For ea…

Let $\widetilde{\mathcal{A}}(p)$, $\widetilde{\mathcal{W}}(p)$, and $\widetilde{\mathcal{W}}^0(p)$ be the vertex algebras constructed inside $V_L$, and let $\mathcal{A}(p)$,…

Let $Q$ be a positive-definite even lattice, let $V_Q$ be its lattice vertex algebra, and let $\sigma$ be an isometry of $Q$ of order two, lifted to an automorphism of $V_Q$. Write…

Let $V_{fer}$ denote the free fermion vertex operator superalgebra, let $k$ be an even positive integer, and let $V_{\mathbb{Z}\alpha}$ be the rank-one lattice vertex operator supe…