3 problems

Tropical tensor-product conjecture. The tropicalization of $F$ is an isomorphism of torsion-free Kashiwara crystals

Schubert-cell crystal conjecture. For every $w\in W$,

Injectivity conjecture. For every connected component of $\mathcal{B}_{f,\Theta}$, the restriction of $\tilde {\bf f}_w$ is injective.