5 problems

Shank–Wehlau–Broer conjecture. If $S^G$ is a direct summand of $S$ as an $S^G$-module, then $S^G$ is a polynomial ring.

Filtration submodule and annihilation conjecture. For each $1\leq k<\min(m,n)$, $\mathcal{F}_{n,k}$ is an $\mathcal{A}$-submodule and a ${\mathcal{D}}_n$-submodule of…

Explicit general-linear basis conjecture. The set $\mathcal{B}_m(n)$ consisting of these elements forms an $\mathbb{F}_q$-basis of ${\mathcal{Q}}_m(n)^{G_n}$. The conjecture is the…

Explicit parabolic basis conjecture. The resulting elements

Let $p$ be the characteristic of the ground field, let $R^{S\!p(n)}$ be the invariant ring for $n\times n$ generic matrices under the symplectic group, and let $K_{\infty}$ denote…