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Existence of Kirillov-Reshetikhin crystals for nonexceptional types

Author(s): Masato Okado; Anne Schilling
Journal: Represent. Theory 12 (2008), 186-207.
MSC (2000): Primary 17B37, 81R50; Secondary 05E15, 81R10
Posted: April 14, 2008
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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 $ r$ not a spin node.

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Additional Information:

Masato Okado
Affiliation: Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Email: okado@sigmath.es.osaka-u.ac.jp

Anne Schilling
Affiliation: Department of Mathematics, University of California, One Shields Avenue, Davis, California 95616-8633
Email: anne@math.ucdavis.edu

DOI: 10.1090/S1088-4165-08-00329-4
PII: S 1088-4165(08)00329-4
Received by editor(s): August 8, 2007
Received by editor(s) in revised form: February 26, 2008
Posted: April 14, 2008
Dedicated: Dedicated to Professor Masaki Kashiwara on his sixtieth birthday
Copyright of article: Copyright 2008, American Mathematical Society

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