RSK correspondence and classically irreducible Kirillov-Reshetikhin crystals

Abstract

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.

25 pages

References in corpus (2)

• Existence of Kirillov-Reshetikhin crystals for nonexceptional types
• Kirillov--Reshetikhin crystals for nonexceptional types

Cited by in corpus (7)

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• Lusztig data of Kashiwara-Nakashima tableaux in type D
• Unipotent quantum coordinate ring and prefundamental representations for types $A_n^{(1)}$ and $D_n^{(1)}$
• A combinatorial realization of Kirillov-Reshetikhin crystals for type E arising from translations
• Kirillov-Reshetikhin crystals $B^{1,s}$ for ${\widehat{\mathfrak{sl}}}_n$ using Nakajima monomials
• Kirillov-Reshetikhin crystals, energy function and the combinatorial R-matrix