2 problems

Generalized Kac–Wakimoto conjecture. Every simple ${\mathfrak{g}}$-supermodule $J$ is ambidextrous. If $L$ is another simple supermodule satisfying

Two-sided trace conjecture. For even ordered $\xi$, there exists a category $\overline{\mathscr{C}}_{even}$ of modules over $\overline{\mathcal U}_\xi^L({\mathfrak{g}})$ such that…