Construction of affine geometric crystals and Representation theory of crystal bases

对于大多数仿射Kac-Moody代数，我们构造了与最简单KR模相关的几何晶体。我们还显式地得到了热带R图。此外，仅对sl(2)情形，构造了某些普适型热带R图。作为几何晶体均匀性的判据，我们证明了超离散得到的晶体是连通的。根据这一准则，可以很容易地显示出热带R图的唯一性。我们得到了A型的epsilon系统。

For most affine Kac-Moody algebras, we constructed geometric crystals associated with the simplest KR modules. We also obtained tropical R maps explicitly. Furthermore, only for sl (2)-case, certain universal type tropical R maps have been constructed. As a criterion for homogeneity of geometric crystals, we showed that the crystal obtained by the ultra-discretization is connected. By this criterion, it turns out that we can show easily the uniqueness of tropical R maps. We got epsilon systems of type A.