5 problems

$E_8(a_7)$ permutation-orbifold conjecture. We have an isomorphism

Let $\mathcal{L}_{-22/5}$ be the simple Virasoro vertex algebra of central charge $-22/5$, and let $S_4$ act on its fourth tensor power by permuting the tensor factors. Write…

Let $A$ be a rational conformal field theory, let $\mathcal{C}=\operatorname{Rep}(A)$, and let $G\leq S_n$ act by permuting the factors of $\mathcal{C}^{\boxtimes n}$. Denote the r…

Let $V$ be a vertex operator superalgebra and let $k$ be a positive even integer. The cyclic permutation $(1\;2\;\cdots\;k)$ acts on the tensor product vertex operator superalgebra…

Let $V$ be a vertex operator superalgebra, let $k$ be even, and let $g=(1\;2\;\cdots\;k)$ act by permuting the tensor factors of $V^{\otimes k}$. A parity-twisted $V$-module is a m…