4 problems

The Rouquier-block multiplicity conjecture. The multiplicity of $L(\boldsymbol{mu})$ as a composition factor of $Delta(\boldsymbol{lambda})$ is

Littlewood–Richardson character conjecture.

Hopf structure and tensor-product conjecture. The algebra $\mathcal{U}_{q,\widetilde{\mathbf Q}}(\mathbf m)$ should have a Hopf algebra structure, and, through $\Psi$ and this stru…

Surjectivity-isomorphism conjecture. The displayed surjective homomorphism is an isomorphism. This would identify the specialization, modulo $\mathfrak J$, with the universal envel…