Affine Geometric Crystals and Limit of Perfect Crystals
  For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect crystals of the Langlands dual affine Lie algebra. 
Masaki Kashiwara, Toshiki Nakashima and Masato Okado