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Existence of Kirillov鈥揜eshetikhin 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鈥揜eshetikhin modules by Nakajima and Hernandez, the existence of Kirillov鈥揜eshetikhin 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
MR Author ID: 352840
ORCID: 0000-0002-2601-7340
Email: anne@math.ucdavis.edu

Received by editor(s): August 8, 2007
Received by editor(s) in revised form: February 26, 2008
Published electronically: April 14, 2008
Dedicated: Dedicated to Professor Masaki Kashiwara on his sixtieth birthday
Article copyright: © Copyright 2008 American Mathematical Society