RSK correspondence and classically irreducible Kirillov–Reshetikhin crystals

We give a new combinatorial model of the Kirillov–Reshetikhin crystals of type A n ( 1 ) in terms of non-negative integral matrices based on the classical RSK algorithm, which has a simple description of the affine crystal structure without using the promotion operator. We have a similar description of the Kirillov–Reshetikhin crystals associated to exceptional nodes in the Dynkin diagrams of classical affine or non-exceptional affine type, which are called classically irreducible together with those of type A n ( 1 ) .