Level 1 Perfect Crystals and Path Realizations of Basic Representations   at q=0
  We present a uniform construction of level 1 perfect crystals $\mathcal B$ for all affine Lie algebras. We also introduce the notion of a crystal algebra and give an explicit description of its multiplication. This allows us to determine the energy function on $\mathcal B \otimes \mathcal B$ completely and thereby give a path realization of the basic representations at $q=0$ in the homogeneous picture. 
Georgia Benkart, Igor Frenkel, Seok-Jin Kang, Hyeonmi Lee