5 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.

Let $\mu$ be as in the paper, let $H_{\mathrm{hw}}$ be the highest-weight element, and write $\ell(\mu)$ for the number of nonzero parts of $\mu$. Assume $n=\max(H_{\mathrm{hw}})$,…

Let $e=2$ and let $\Lambda=a\Lambda_0+a\Lambda_1$. Let $\mu$ be an $e$-regular multipartition reached by a path $p$ stabilizing at $t$, of length $w$, with … Let $t'$ be the first…