Abstract
We give a new combinatorial model of the Kirillov–Reshetikhin crystals of type An(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 An(1).
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