7 problems

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

Shang's conjecture. For $k>1$, the $\mathfrak{sl}_3$-module

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

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

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

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

Let $Alt[X]$ be the free alternative algebra, let $Z=Z(Alt[X])$ denote its center, and regard the degree of an element as its total degree in the free generators. Filippov's conjec…