Quantized affine algebras and crystals with core

Motivated by the work of Nakayashiki on the inhomogeneous vertex models of 6-vertex type, we introduce the notion of crystals with core. We show that the tensor product of the highest weight crystal B(5) of level k and the perfect crystal Bl of level l is isomorphic to the tensor product of the perfect crystal Bl m k of level lm k and the highest weight crystal B(5') of level k