4 problems

Shang's character-formula conjecture. In the Grothendieck ring of $GL(V)$,

Additive-map factorization conjecture. There exists a fixed element $q\in D$ such that

Invariant-homology conjecture. As $sl_3(k)$-modules,

Dimension-generating-series conjecture. Suppose $a(z)$ and $b(z)$ are the solutions of