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
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by Masato Okado and Anne Schilling

Represent. Theory 12 (2008), 186-207

DOI: https://doi.org/10.1090/S1088-4165-08-00329-4

Published electronically: April 14, 2008

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Erratum: Represent. Theory 12 (2008), 499-500.

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 $r$ not a spin node.

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