Geodesic
Kirillov-Reshetikhin crystals, energy function and the combinatorial $R$-matrix
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 45-74.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We study the polytope model for the affine type $A$ Kirillov-Reshetikhin crystals and prove that the action of the affine Kashiwara operators can be described in a remarkably simple way. Moreover, we investigate the combinatorial $R$-matrix on a tensor product of polytopes and characterize the map explicitly on the highest weight elements. We further give a formula for the local energy function and provide an alternative proof for the perfectness. We determine for any dominant highest weight element $\Lambda $ of level $\ell $ the elements $b_{\Lambda}, b^{\Lambda}$ involved in the definition of perfect crystals and give an explicit description of the ground-state path in the tensor product of polytopes.
Classification : 17B37, 05E15, 17B67
Keywords: KR crystal, energy function, $R$-matrix 
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     title = {Kirillov-Reshetikhin crystals, energy function and the combinatorial $R$-matrix},
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Kus, Deniz. Kirillov-Reshetikhin crystals, energy function and the combinatorial $R$-matrix. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 45-74. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a8/