Polyhedral Realizations of Crystal Bases for Integrable Highest Weight   Modules
  We give a general way of representing the crystal (base) corresponding to the intgrable highest weight modules of quantum Kac-Moody algebras, which is called polyhedral realizations. This is applied to describe explicitly the crystal bases of integrable highest weight modules for arbitrary rank 2 Kac-Moody algebra cases, the classical A_n-case and the affine A^{(1)}_{n-1}-case. 
Toshiki Nakashima (Sophia Univ.)