RSK correspondence and classically irreducible Kirillov-Reshetikhin crystals

Details RSK correspondence and classically irreducible Kirillov-Reshetikhin crystals RSK correspondence and classically irreducible Kirillov-Reshetikhin crystals

2011-10-12

arxiv.org/abs/1110.2629v2

Mathematics

Quantum Algebra

25 pages

Scientific paper

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 a promotion operator. We also have a similar description of the Kirillov-Reshetikhin crystals associated to exceptional nodes in the Dynkin diagrams of classical affine or non-exceptional type.

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