4 problems

Coherent-family limit conjecture. The crystal ${\mathcal UD}(\chi,T,\theta)$ is the limit of a coherent family of perfect crystals of type $\TY(G,1,2)$ in the cited work.

Let $\mathfrak g$ be an affine Kac–Moody algebra with index set $I$, distinguished node $0$, Weyl group $W$, extended Weyl group $\widetilde W$, and Langlands dual $\mathfrak g^L$.…

Let $\{B^l\}_{l\geq 1}$ be a coherent family of perfect crystals, with limit crystal $B^\infty$ and distinguished element $b_\infty$. Let $P_{cl}$ be the classical weight lattice,…

KNO conjecture. The affine Lie algebra $\mathfrak g$ has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of a certain coherent family of perfect…