5 problems

Binary-operation conjecture. $\pi(C_1*C_2)$ is a subrepresentation of $\pi(C_1)\times\pi(C_2)$. In particular, if $\pi(C_1)$ or $\pi(C_2)$ is $\square$-irreducible, then

Reducedness conjecture. The scheme $\overline N$ is reduced. This reducedness assertion is used to identify the special fiber of the canonical flat model and to establish its norma…

Let $C_i\in\operatorname{Comp}(\bm{d}_i)$ for $i=1,\dots,k$, let $V=V^1\oplus\cdots\oplus V^k$, and let $C\in\operatorname{Comp}(V)$. Let $\pi(C)$ denote the irreducible representa…

Let $C_i\in\operatorname{Comp}(\bm{d}_i)$ for $i=1,2$, and suppose that at least one of $C_1,C_2$ is rigid, meaning that it contains an open orbit. Let $\pi(C_i)$ be the correspond…

Monotonicity conjecture. If $C_r(\mathcal{N}_n)$ is reducible, then $C_r(\mathcal{N}_{n+1})$ is reducible.