Weight-semigroup group conjecture for semi-invariants of parabolic contractions

Let $\operatorname{\mathfrak{q}}$ be a parabolic contraction, and let $\Lambda$ be the semigroup of weights of its semi-invariant algebra $\operatorname{Sy}(\operatorname{\mathfrak{q}})$. Weight-semigroup group conjecture. The semigroup $\Lambda$ is a group.

This conjecture asserts that every weight occurring in the semi-invariant algebra is compatible with group structure, rather than merely forming a semigroup. The paper notes that all parabolic contractions studied so far have this property, but supplies no general proof or resolution.