4 problems

Let $\mathfrak{g}$ be an affine Lie algebra with Dynkin index set $I$, and let $i\in I\setminus\{0\}$. A positive geometric crystal for $\mathfrak{g}$ is a quadruple … where $X$ is…

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.

KNO conjecture. For any $i\in I\setminus\{0\}$, there exists a unique variety $X$ endowed with a positive $\mathfrak g$-geometric crystal structure and a rational map…

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…