3 problems

Let $F$ be a field, let $G$ be a finite group, and let $M$ be an $F G$-module. Write $M^*$ for the dual module, and let $\gamma_G$ denote the gamma invariant for $F G$-modules. Ben…

Period conjecture. The minimum period of $\psi_\Lambda^n$ is $e$ or $2e$, and the minimum period of $\psi_S^n$ is $e$ or $2e$.

Thévenaz's conjecture. An analogous Brauer–Berman–Witt theorem should hold for $\operatorname{gr}(kG)$.