Existence of Kirillov–Reshetikhin crystals for nonexceptional types

Okado, Masato; Schilling, Anne

doi:10.1090/S1088-4165-08-00329-4

Existence of Kirillov-Reshetikhin crystals for nonexceptional types

Authors: Masato Okado and Anne Schilling
Journal: Represent. Theory 12 (2008), 186-207
MSC (2000): Primary 17B37, 81R50; Secondary 05E15, 81R10
DOI: https://doi.org/10.1090/S1088-4165-08-00329-4
Published electronically: April 14, 2008
Erratum: Represent. Theory 12 (2008), 499--500
MathSciNet review: 2403558
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Abstract: Using the methods of Kang et al. and recent results on the characters of Kirillov-Reshetikhin modules by Nakajima and Hernandez, the existence of Kirillov-Reshetikhin crystals $B^{r,s}$ is established for all nonexceptional affine types. We also prove that the crystals $B^{r,s}$ of type $B_n^{(1)}$ , $D_n^{(1)}$ , and $A_{2n-1}^{(2)}$ are isomorphic to recently constructed combinatorial crystals for not a spin node.

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