6 problems

Steinberg tensor product conjecture. Any irreducible representation of $G$ is uniquely a tensor product of a one-irreducible representation and one inflated from $G_0$.

Classification conjecture. Every incompressible category of moderate growth over $\mathbf{k}$ is a tensor subcategory of $\mathsf{Ver}_{p^\infty}$.

Let $p>0$, let ${\rm Ver}_p^+$ be the relevant Verlinde category, and let $\mathfrak{g}$ be a simple Lie algebra in ${\rm Ver}_p^+$ containing a simple Lie algebra $\mathfrak{s}$ s…

Let $p\geq5$, let ${\rm Ver}_p$ be the Verlinde category, and let $G$ be a simple linearly reductive height-$1$ group scheme in ${\rm Ver}_p$, with Lie algebra…

Let $p\geq5$, let ${\rm Ver}_p$ be the Verlinde category, and let $G$ be a linearly reductive height-$1$ subgroup scheme of $GL(Y)$ for an object $Y\in {\rm Ver}_p$. Let…

Assume that $p>0$. A pre-Tannakian category is a $\boldsymbol{k}$-linear, rigid, symmetric monoidal abelian category with finite-dimensional Hom spaces and finite length objects. I…