4 problems

The nqc-type conjecture. The composition factors of $\overline{V}(\Lambda)$ are in one-to-one correspondence with the codes $\Sigma^c$ determined from $nqc(\Lambda)$, with the code…

Hughes' permissible-code conjecture. There is a bijection between the composition factors of $\overline{V}(\Lambda)$ and the permissible codes.

Let ${\mathfrak {gl}}_{m|n}$ be the general linear Lie superalgebra, let $\kac{\lambda}$ be a Kac-module, and let permissible codes be the combinatorial objects defined in Definiti…

Let $\mathfrak{g}$ be a type I Lie superalgebra, let $u\neq 0$ satisfy $[u,u]=0$, and let $\mathbb{O}\subseteq\widetilde{G_u}$ be the purely odd supergroup with Lie superalgebra…