Decorated Geometric Crystals, Polyhedral and Monomial Realizations of   Crystal Bases
  We shall show that for type $A_n$ the realization of crystal bases obtained from the decorated geometric crystals intorduced by Berenstein and Kazhdan coincides with our polyhedral realizations of crystal bases. We also observe certain relations of decorations and monomial realizations of crystal bases. 
Toshiki Nakashima
math.QA math.RT