Geometric crystals and Cluster ensembles in Kac-Moody setting

Yuki Kanakubo, Toshiki Nakashima

For a Kac-Moody group $G$, double Bruhat cells $G^{u,e}$ ($u$ is a Weyl group element) have positive geometric crystal structures. In arXiv:1210.2533, it is shown that there exist…