HALF POTENTIAL ON GEOMETRIC CRYSTALS AND CONNECTEDNESS OF CELLULAR CRYSTALS

Geometric and Unipotent Crystals

Rhombellanic Crystals and Quasicrystals

Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

0 Geometric and Unipotent Crystals

Lecture Notes on Geometric Crystals and Their Combinatorial Analogues

The first author would like to express his gratitude to Professor Okado for the opportunity to give the lectures, to Professor Kuniba for the great help in preparation of the lecture notes, and to RIMS for the hospitality. The lectures are based on the results of our research originated six years ago in [1] and continued in [2]. We start with the problem of birational Weyl group actions that se...

Epsilon Systems on Geometric Crystals of type A n ?

We introduce an epsilon system on a geometric crystal of type An, which is a certain set of rational functions with some nice properties. We shall show that it is equipped with a product structure and that it is invariant under the action of tropical R maps.